There is some background material on Socrates in the Wikipedia.  There is a good site at Clarke University, the Last Days of Socrates, that presents the Platonic dialogues set during the last period of Socrates' life, though for some strange reason it only includes the end of the Phaedo.  For general discussion of Socrates you could try here (Russo) or here (Cannon).  There is a commentary on the Apology here (Humphrey), here (Kelley Ross) and here (Russo). Wedgwood has commentaries on the Apology, the Euthyphro, and Book 1 of the Republic.  N.D. Smith has a review of a book about Socrates' trial that gives a good picture of some of the the issues.

For an adverse reaction to Socrates, see David Fielding's essay. Macdonald Ross has a different view of the relation between Socrates and Plato.

For an interesting angle on Socrates, as Educator, and on the import of classicism more generally, two essays by the early 20th century Australian philosopher, John Anderson, are now available on-line.

Socrates claims to have lived his life fulfilling what he took to be a divine mission. An impulsive friend had asked Apollo's oracle at Delphi whether there was anyone wiser than Socrates. The answer was that no one was wiser than him. Here is what Socrates then said, in Jowett's translation (taken from the Last days of Socrates site at Clarke University):

When I heard the answer, I said to myself, What can the god mean? and what is the interpretation of his riddle? for I know that I have no wisdom, small or great. What then can he mean when he says that I am the wisest of men? And yet he is a god, and cannot lie; that would be against his nature. After long consideration, I thought of a method of trying the question. I reflected that if I could only find a man wiser than myself, then I might go to the god with a refutation in my hand. I should say to him, "Here is a man who is wiser than I am; but you said that I was the wisest." Accordingly I went to one who had the reputation of wisdom, and observed him — his name I need not mention; he was a politician whom I selected for examination — and the result was as follows: When I began to talk with him, I could not help thinking, that he was not really wise, although he was thought wise by many, and still wiser by himself; and thereupon I tried to explain to him that he thought himself wise, but was not really wise; and the consequence was that he hated me, and his enmity was shared by several who were present and heard me. So I left him, saying to myself, as I went away: Well, although I do not suppose that either of us knows anything really beautiful and good, I am better off than he is for he knows nothing, and thinks that he knows; I neither know nor think that I know. In this latter particular then, I seem to have slightly the advantage of him. Then I went to another who had still higher pretensions to wisdom, and my conclusion was exactly the same. Whereupon I made another enemy of him, and of many others besides him. [21b-e]

At last I went to the artisans, for I was conscious that I knew nothing at all, as I may say, and I was sure that they knew many fine things; and here I was not mistaken, for they did know many things of which I was ignorant, and in this they certainly were wiser than I was. But I observed that even the good artisans fell into the same error as the poets; — because they were good workmen they thought that they also knew all sorts of high matters, and this deceit in them overshadowed their wisdom; and therefore I asked myself on behalf of the oracle, whether I would like to be as I was, neither having their knowledge nor their ignorance, or like them in both; and I made answer to myself and to the oracle that I was better off as I was. [22d-e]

This inquisition has led to my having many enemies of the worst and most dangerous kind, and has given occasion also to many calumnies. And I am called wise, for my hearers always imagine that I myself possess the wisdom which I find wanting in others: but the truth is, O men of Athens, that God only is wise; and by his answer he intends to show that the wisdom of men is worth little or nothing; he is not speaking of Socrates, he is only using my name by way of illustration, as if he said, He, O men, is the wisest, who, like Socrates, knows that his wisdom is in truth worth nothing. And so I go about the world, obedient to the God, and search and make enquiry into the wisdom of any one, whether citizen or stranger, who appears to be wise; and if he is not wise, then in vindication of the oracle I show him that he is not wise; and my occupation quite absorbs me, and I have had no time to do anything useful either in public affairs or in any concern of my own, but I am in utter poverty by reason of my devotion to the god. [23a-c, translation adapted from revised 1955 edition]

He later adds that if the jury were to let him go free on condition that he stop his questioning:

I should reply: Athenians, I honor and love you; but I shall obey God rather than you, and while I have life and strength I shall never cease from the practice and teaching of philosophy, exhorting any one whom I meet and saying to him after my manner: You, my friend, — a citizen of the great and mighty and wise city of Athens, — are you not ashamed of heaping up the greatest amount of money and honor and reputation, and caring so little about wisdom and truth and the greatest improvement of the soul, which you never regard or heed at all? And if the person with whom I am arguing, says: Yes, but I do care; then I do not leave him or let him go at once; but I proceed to interrogate and examine and cross-examine him, and if I think that he has no virtue in him, but only says that he has, I reproach him with undervaluing the greater, and overvaluing the less. And I shall repeat the same words to every one whom I meet, young and old, citizen and alien, but especially to the citizens, inasmuch as they are my brethren. For know that this is the command of God; and I believe that no greater good has ever happened in the state than my service to the God. For I do nothing but go about persuading you all, old and young alike, not to take thought for your persons or your properties, but first and chiefly to care about the greatest improvement of the soul. I tell you that virtue is not given by money, but that from virtue comes money and every other good of man, public as well as private. [I am convinced by Vlastos (p. 219, ftn. 73) that this is a misconstrual of the text. He translates: "For virtue does not come from wealth, but through virtue, wealth and everything else, private and public, become good for men" — which does not make Socrates suppose virtue is a way of making money.] This is my teaching, and if this is the doctrine which corrupts the youth, I am a mischievous person. But if any one says that this is not my teaching, he is speaking an untruth. [29d-30b]

For if you kill me you will not easily find a successor to me, who, if I may use such a ludicrous figure of speech, am a sort of gadfly, given to the state by God; and the state is a great and noble stead who is tardy in his motions owing to his very size, and requires to be stirred into life. I am that gadfly which God has attached to the state, and all day long and in all places am always fastening upon you, arousing and persuading and reproaching you. [30e-31a]

Though the Apology is not often cited as an example of Socratic argument, we can see the sort of thing Socrates did from his replies to the specific charges brought against him (he keeps warning the jurors not to take offence if they see him behaving in his accustomed manner):

He says that I am a doer of evil, and corrupt the youth; but I say, O men of Athens, that Meletus is a doer of evil, in that he pretends to be earnest when he is only in jest, and is so eager to bring men to trial from a pretended zeal and interest about matters in which he really never had the smallest interest. And the truth of this I endeavor to prove to you.
Come hither, Meletus, and let me ask a question of you. You think a great deal about the improvement of youth?
Meletus: Yes, I do.
Socrates: Tell the judges, then, who is their improver; for you must know, as you have taken the pains to discover their corrupter, and are citing and accusing me before them. Speak then and tell the judges who their improver is. — Observe, Meletus that you are silent, and have nothing to say. But is not this rather disgraceful, and a very considerable proof of what I was saying, that you have no interest in the matter? Speak up, friend, and tell us who their improver is.
Mel: The laws.
Soc: But that, my good sir, is not my meaning. I want to know who the person is, who, in the first place, knows the laws.
Mel: The judges, Socrates, who are present in court.
Soc: What, do you mean to say, Meletus, that they are able to instruct and improve youth?
Mel: Certainly they are.
Soc: What, all of them, or some only and not others?
Mel: All of them.
Soc: By the goddess, Hera, that is good news! There are plenty of improvers, then. And what do you say of the audience, do they improve them?
Mel: Yes, they do.
Soc: And the senators?
Mel: Yes, the senators improve them.
Soc: But perhaps the members of the assembly corrupt them? — or do they too improve them?
Mel: They improve them.
Soc: Then every Athenian improves and elevates them; all with the exception of myself, and I alone am their corrupter? Is that what you affirm?
Mel: That is what I stoutly affirm.
Soc: I am very unfortunate if you are right. But suppose I ask you a question: How about horses? Does one man do them harm and all the world good? Is not the exact opposite the truth? One man is able to do them good, or at least not many; — the trainer of horses, that is to say, does them good, and others who have to do with them rather injure them? Is not that true, Meletus, of horses, or of any other animals? Most assuredly it is; whether you and Anytus say yes or no. Happy indeed would be the condition of youth if they had one corrupter only, and all the rest of the world were their improvers. But you, Meletus, have sufficiently shown that you never had a thought about the young: your carelessness is seen in your not caring about the very things which you bring against me.
And now, Meletus, I will ask you another question — by Zeus I will: Which is better, to live among bad citizens, or among good ones? Answer, friend. I say, the question is one which may be easily answered. Do not the good do their neighbours good, and the bad do them evil?
Mel: Certainly.
Soc: And is there any one who would rather be injured than benefitted by those who live with him? Answer, my good friend, the law requires you to answer — does any one like to be injured?
Mel: Certainly not.
Soc: And when you accuse me of corrupting and deteriorating the youth, do you allege that I corrupt them intentionally or unintentionally?
Mel: Intentionally, I say.
Soc: But you have just admitted that the good do their neighbours good and evil do them evil. Now, is that a truth which your superior wisdom has recognized this early in life, and am I, at my age, in such darkness and ignorance as not to know that if a man with whom I have to live is corrupted by me, I am very likely to be harmed by him; and yet I corrupt him, and intentionally, too — so you say, although neither I nor any other human being is ever likely to be convinced by you. But either I do not corrupt them, or I corrupt them unintentionally; and on either view of the case you lie. If my offence is unintentional, the law has no cognizance of unintentional offenses: you ought to have taken me privately, and warned and admonished me, for if I had been better advised, I should have left off doing what I only did unintentionally — no doubt I should; but you would have nothing to say to me and refused to teach me. And now you bring me up in this court, which is a place not of instruction, but of punishment. [24c-26a]

Whatever the merits of these moves, we can see the presenting of alternatives (all or some? intentionally or unintentionally? — very often binary pairs) that are to be used as dilemmas, each alternative leading to a conclusion unwanted by Socrates' opponent, and the fondness for analogies taken from everyday pursuits (here horse-training). A little later, Socrates attempts to lead Meletus into pure self-contradiction:

Did ever man, Meletus, believe in the existence of human things, and not of human beings? .... Did ever any man believe in horsemanship, and not in horses? or in flute-playing, and not in flute-players? No, my friend; I will answer to you and to the court, as you refuse to answer for yourself. There is no man who ever did. But now please to answer the next question: Can a man believe in spiritual and divine agencies, and not in spirits or demigods?
Mel. He cannot.
Soc. How lucky I am to have extracted that answer, by the assistance of the court! But then you swear in the indictment that I teach and believe in divine or spiritual agencies (new or old, no matter for that); at any rate, I believe in spiritual agencies, — so you say and swear in the affidavit; and yet if I believe in divine beings, how can I help believing in spirits or demigods; — must I not? To be sure I must; and therefore I may assume that your silence gives consent. Now what are spirits or demigods? are they not either gods or the sons of gods.
Mel. Certainly they are.
Soc. But this is what I call the facetious riddle invented by you: the demigods or spirits are gods, and you say first that I do not believe in gods, and then again that I do believe in gods; that is, if I believe in demigods. For if the demigods are the other illegitimate sons of gods, whether by the nymphs or by any mothers, of whom they are said to be the sons — what human being will ever believe that there are no gods if they are the sons of gods? You might as well affirm the existence of mules, and deny that of horses and asses. [27b-e]

Let us look at some other examples of the Socratic elenchos in operation, in some of the dialogues commonly agreed to be early and to reflect the sort of activity the historic Socrates engaged in. The first is from the Euthyphro, in which Socrates is seeking to discover the nature of piety from Euthyphro, who is engaged in prosecuting his own father for the murder of one of his serfs [from Jowett's translation at Virginia Tech]:

And therefore, I adjure you to tell me the nature of piety and impiety, which you said that you knew so well, and of murder, and of other offences against the gods. What are they? Is not piety in every action always the same? and impiety, again — is it not always the opposite of piety, and also the same with itself, having, as impiety, one notion which includes whatever is impious?
Euth. To be sure, Socrates.
Soc. And what is piety, and what is impiety?
Euth. Piety is doing as I am doing; that is to say, prosecuting any one who is guilty of murder, sacrilege, or of any similar crime — whether he be your father or mother, or whoever he may be — that makes no difference; and not to prosecute them is impiety....
Soc. But just at present I would rather hear from you a more precise answer, which you have not as yet given, my friend, to the question, What is "piety"? When asked, you only replied, Doing as you do, charging your father with murder.
Euth. And what I said was true, Socrates.
Soc. No doubt, Euthyphro; but you would admit that there are many other pious acts?
Euth. There are.
Soc. Remember that I did not ask you to give me two or three examples of piety, but to explain the general idea which makes all pious things to be pious. Do you not recollect that there was one idea which made the impious impious, and the pious pious?
Euth. I remember.
Soc. Tell me what is the nature of this idea, and then I shall have a standard to which I may look, and by which I may measure actions, whether yours or those of any one else, and then I shall be able to say that such and such an action is pious, such another impious....
Euth. Piety, then, is that which is dear to the gods, and impiety is that which is not dear to them.
Soc. Very good, Euthyphro; you have now given me the sort of answer which I wanted. But whether what you say is true or not I cannot as yet tell,.... Let us examine what we are saying. That thing or person which is dear to the gods is pious, and that thing or person which is hateful to the gods is impious, these two being the extreme opposites of one another....Further, Euthyphro, the gods were admitted to have enmities and hatreds and differences?
Euth. Yes, that was also said.
Soc. And what sort of difference creates enmity and anger? Suppose for example that you and I, my good friend, differ about a number; do differences of this sort make us enemies and set us at variance with one another? Do we not go at once to arithmetic, and put an end to them by a sum?
Euth. True.
Soc. Or suppose that we differ about magnitudes, do we not quickly end the differences by measuring?
Euth. Very true.
Soc. And we end a controversy about heavy and light by resorting to a weighing machine?
Euth. To be sure.
Soc. But what differences are there which cannot be thus decided, and which therefore make us angry and set us at enmity with one another? I dare say the answer does not occur to you at the moment, and therefore I will suggest that these enmities arise when the matters of difference are the just and unjust, good and evil, honourable and dishonourable. Are not these the points about which men differ, and about which when we are unable satisfactorily to decide our differences, you and I and all of us quarrel, when we do quarrel?
Euth. Yes, Socrates, ....
Soc. And the quarrels of the gods, noble Euthyphro, when they occur, are of a like nature?
Euth. Certainly they are.
Soc. They have differences of opinion, as you say, about good and evil, just and unjust, honourable and dishonourable: there would have been no quarrels among them, if there had been no such differences — would there now?
Euth. You are quite right.
Soc. Does not every man love that which he deems noble and just and good, and hate the opposite of them?
Euth. Very true.
Soc. But, as you say, people regard the same things, some as just and others as unjust, — about these they dispute; and so there arise wars and fightings among them.
Euth. Very true.
Soc. Then the same things are hated by the gods and loved by the gods, and are both hateful and dear to them?
Euth. True.
Soc. And upon this view the same things, Euthyphro, will be pious and also impious?
Euth. So I should suppose.
Soc. Then, my friend, I remark with surprise that you have not answered the question which I asked. For I certainly did not ask you to tell me what action is both pious and impious: but now it would seem that what is loved by the gods is also hated by them. And therefore, Euthyphro, in thus chastising your father you may very likely be doing what is agreeable to Zeus but disagreeable to Cronos or Uranus,....
Euth. But I believe, Socrates, that all the gods would be agreed as to the propriety of punishing a murderer: there would be no difference of opinion about that....
Soc. I will suppose, if you like, that all the gods condemn and abominate such an action. But I will amend the definition so far as to say that what all the gods hate is impious, and what they love pious or holy; and what some of them love and others hate is both or neither. Shall this be our definition of piety and impiety? ....
Euth. Yes, I should say that what all the gods love is pious and holy, and the opposite which they all hate, impious.
Soc. Ought we to enquire into the truth of this, Euthyphro, or simply to accept the mere statement on our own authority and that of others? .... The point which I should first wish to understand is whether the pious or holy is beloved by the gods because it is holy, or holy because it is beloved of the gods.
Euth. I do not understand your meaning, Socrates.
Soc. I will endeavour to explain: [Socrates gives a somewhat obscure explanation, one point in which is that "the state of being loved follows the act of being loved, and not the act the state."] is not piety, according to your definition, loved by all the gods?
Euth. Yes.
Soc. Because it is pious or holy, or for some other reason?
Euth. No, that is the reason.
Soc. It is loved because it is holy, not holy because it is loved?
Euth. Yes.
Soc. And that which is dear to the gods is loved by them, and is in a state to be loved of them because it is loved of them?
Euth. Certainly.
Soc. Then that which is dear to the gods, Euthyphro, is not holy, nor is that which is holy loved of God, as you affirm; but they are two different things.
Euth. How do you mean, Socrates?
Soc. I mean to say that the holy has been acknowledged by us to be loved of God because it is holy, not to be holy because it is loved.
Euth. Yes.
Soc. But that which is dear to the gods is dear to them because it is loved by them, not loved by them because it is dear to them.
Euth. True.
Soc. But, friend Euthyphro, if that which is holy is the same with that which is dear to God, and is loved because it is holy, then that which is dear to God would have been loved as being dear to God; but if that which is dear to God is dear to him because loved by him, then that which is holy would have been holy because loved by him. But now you see that the reverse is the case, and that they are quite different from one another. For one (theophiles) is of a kind to be loved because it is loved, and the other (hosion) is loved because it is of a kind to be loved. Thus you appear to me, Euthyphro, when I ask you what is the essence of holiness, to offer an attribute only, and not the essence — the attribute of being loved by all the gods. But you still refuse to explain to me the nature of holiness. And therefore, if you please, I will ask you not to hide your treasure, but to tell me once more what holiness or piety really is, whether dear to the gods or not (for that is a matter about which we will not quarrel) and what is impiety?
Euth. I really do not know, Socrates, how to express what I mean. For somehow or other our arguments, on whatever ground we rest them, seem to turn round and walk away from us. [5d-11b]

Here is another example, this time from the Protagoras [Jowett's translation, copied from the Virginia Tech site], which ends a discussion of one of Socrates' favourite issues — can virtue be taught? — with a classic aporia, both participants in the dialogue affirming the opposite of what they started from:

He said: You will find, Socrates, that some of the most impious, and unrighteous, and intemperate, and ignorant of men are among the most courageous; which proves that courage is very different from the other parts of virtue. I was surprised at his saying this at the time, and I am still more surprised now that I have discussed the matter with you. So I asked him whether by the brave he meant the confident. Yes, he replied, and the impetuous or goers. (You may remember, Protagoras, that this was your answer.)
He assented.
Well then, I said, tell us against what are the courageous ready to go — against the same dangers as the cowards?
No, he answered.
Then against something different?
Yes, he said.
Then do cowards go where there is safety, and the courageous where there is danger?
Yes, Socrates, so men say.
Very true, I said. But I want to know against what do you say that the courageous are ready to go — against dangers, believing them to be dangers, or not against dangers?
No, said he; the former case has been proved by you in the previous argument to be impossible.
That, again, I replied, is quite true. And if this has been rightly proven, then no one goes to meet what he thinks to be dangers, since the want of self-control, which makes men rush into dangers, has been shown to be ignorance.
He assented.
And yet the courageous man and the coward alike go to meet that about which they are confident; so that, in this point of view, the cowardly and the courageous go to meet the same things.
And yet, Socrates, said Protagoras, that to which the coward goes is the opposite of that to which the courageous goes; the one, for example, is ready to go to battle, and the other is not ready.
And is going to battle honourable or disgraceful? I said.
Honourable, he replied.
And if honourable, then already admitted by us to be good; for all honourable actions we have admitted to be good.
That is true; and to that opinion I shall always adhere.
True, I said. But which of the two are they who, as you say, are unwilling to go to war, which is a good and honourable thing?
The cowards, he replied.
And what is good and honourable, I said, is also pleasant?
It has certainly been acknowledged to be so, he replied.
And do the cowards knowingly refuse to go to the nobler, and pleasanter, and better?
The admission of that, he replied, would belie our former admissions.
But does not the courageous man also go to meet the better, and pleasanter, and nobler?
That must be admitted.
And the courageous man has no base fear or base confidence?
True, he replied.
And if not base, then honourable?
He admitted this.
And if honourable, then good?
Yes.
But the fear and confidence of the coward or foolhardy or madman, on the contrary, are base?
He assented.
And these base fears and confidences originate in ignorance and uninstructedness?
True, he said.
Then as to the motive from which the cowards act, do you call it cowardice or courage?
I should say cowardice, he replied.
And have they not been shown to be cowards through their ignorance of dangers?
Assuredly, he said.
And because of that ignorance they are cowards?
He assented.
And the reason why they are cowards is admitted by you to be cowardice?
He again assented.
Then the ignorance of what is and is not dangerous is cowardice?
He nodded assent.
But surely courage, I said, is opposed to cowardice?
Yes.
Then the wisdom which knows what are and are not dangers is opposed to the ignorance of them?
To that again he nodded assent.
And the ignorance of them is cowardice?
To that he very reluctantly nodded assent.
And the knowledge of that which is and is not dangerous is courage, and is opposed to the ignorance of these things?
At this point he would no longer nod assent, but was silent.
And why, I said, do you neither assent nor dissent, Protagoras?
Finish the argument by yourself, he said.
I only want to ask one more question, I said. I want to know whether you still think that there are men who are most ignorant and yet most courageous?
You seem to have a great ambition to make me answer, Socrates, and therefore I will gratify you, and say, that this appears to me to be impossible consistently with the argument.
My only object, I said, in continuing the discussion, has been the desire to ascertain the nature and relations of virtue; for if this were clear, I am very sure that the other controversy which has been carried on at great length by both of us — you affirming and I denying that virtue can be taught — would also become clear. The result of our discussion appears to me to be singular. For if the argument had a human voice, that voice would be heard laughing at us and saying: "Protagoras and Socrates, you are strange beings; there are you, Socrates, who were saying that virtue cannot be taught, contradicting yourself now by your attempt to prove that all things are knowledge, including justice, and temperance, and courage, — which tends to show that virtue can certainly be taught; for if virtue were other than knowledge, as Protagoras attempted to prove, then clearly virtue cannot be taught; but if virtue is entirely knowledge, as you are seeking to show, then I cannot but suppose that virtue is capable of being taught. Protagoras, on the other hand, who started by saying that it might be taught, is now eager to prove it to be anything rather than knowledge; and if this is true, it must be quite incapable of being taught." [359b-361c]

Finally, let us look at a short section of one of the arguments in Book 1 of the Republic, a chapter that is often regarded as of much earlier date than the rest of that work. At this point, Thrasymachus enters the debate and offers an account of justice [Jowett's translation copied from the Evansville site]:

Listen, then, he said; I proclaim that justice is nothing else than the interest of the stronger. And now why do you not praise me? But of course you won't.
Let me first understand you, I replied. Justice, as you say, is the interest of the stronger. What, Thrasymachus, is the meaning of this? You cannot mean to say that because Polydamas, the pancratiast, is stronger than we are, and finds the eating of beef conducive to his bodily strength, that to eat beef is therefore equally for our good who are weaker than he is, and right and just for us?
That's abominable of you, Socrates; you take the words in the sense which is most damaging to the argument.
Not at all, my good sir, I said; I am trying to understand them; and I wish that you would be a little clearer.
Well, he said, have you never heard that forms of government differ; there are tyrannies, and there are democracies, and there are aristocracies?
Yes, I know.
And the government is the ruling power in each state?
Certainly.
And the different forms of government make laws democratical, aristocratical, tyrannical, with a view to their several interests; and these laws, which are made by them for their own interests, are the justice which they deliver to their subjects, and him who transgresses them they punish as a breaker of the law, and unjust. And that is what I mean when I say that in all states there is the same principle of justice, which is the interest of the government; and as the government must be supposed to have power, the only reasonable conclusion is, that everywhere there is one principle of justice, which is the interest of the stronger.
Now I understand you, I said; and whether you are right or not I will try to discover. But let me remark, that in defining justice you have yourself used the word "interest" which you forbade me to use. It is true, however, that in your definition the words "of the stronger" are added.
A small addition, you must allow, he said.
Great or small, never mind about that: we must first enquire whether what you are saying is the truth. Now we are both agreed that justice is interest of some sort, but you go on to say "of the stronger"; about this addition I am not so sure, and must therefore consider further.
Proceed.
I will; and first tell me, Do you admit that it is just for subjects to obey their rulers?
I do.
But are the rulers of states absolutely infallible, or are they sometimes liable to err?
To be sure, he replied, they are liable to err.
Then in making their laws they may sometimes make them rightly, and sometimes not?
True.
When they make them rightly, they make them agreeably to their interest; when they are mistaken, contrary to their interest; you admit that?
Yes.
And the laws which they make must be obeyed by their subjects, — and that is what you call justice?
Doubtless.
Then justice, according to your argument, is not only obedience to the interest of the stronger but the reverse?
What is that you are saying? he asked.
I am only repeating what you are saying, I believe. But let us consider: Have we not admitted that the rulers may be mistaken about their own interest in what they command, and also that to obey them is justice? Has not that been admitted?
Yes.
Then you must also have acknowledged justice not to be for the interest of the stronger, when the rulers unintentionally command things to be done which are to their own injury. For if, as you say, justice is the obedience which the subject renders to their commands, in that case, O wisest of men, is there any escape from the conclusion that the weaker are commanded to do, not what is for the interest, but what is for the injury of the stronger?
Nothing can be clearer, Socrates, said Polemarchus. [338c-340]

For discussion by others of these questions, you can consult Rob Reich, "Confusion about the Socratic Method: Socratic Paradoxes and Contemporary Invocations of Socrates" from the Philosophy of Education Society Yearbook for 1998, with a reply by Betty Sichel.

For some detailed comments on Socratic definitions, see Cohen's lecture. I have some elementary remarks on definitions here.

The second passage from Aristotle credits Socrates with another first: epagogic arguments. This term is often rendered as "inductive", but Vlastos (pp. 267-9) points out that this is very misleading. Rather it is a kind of argument from analogy where one exhibits the meaning of a general statement by exemplifying instances of it. So Socrates argues (Ion 540b-d) that the doctor is the one who knows best what should be said to the sick, the military expert knows best what to say to the troops,... so the master of a craft knows best about matters falling within its subject-matter. Here the instances are not being used as a basis for a merely inductive leap to a general conclusion (doctors are male; generals are male; ... so all experts are male), they are not bits of empirical evidence for the general statement, but are bringing home to us exactly what it means.

A brief remark about irony: Vlastos, whose account of Socrates' denial of knowledge I have been following, notes that while simple irony is a matter of saying p with the intention of being understood to mean the opposite there is a more complex form, that he thinks is exemplified by Socrates, where the asserted p is intended to be understood as denied in one sense, but equally affirmed in another (Socrates: Ironist and Moral Philosopher, Cambridge: CUP, 1991, ch. 1). One illustration is taken from Xenophon's report that Socrates claimed his bulging eyes were beautiful: in conventional terms he knew they weren't, but as far as fulfilling their function went, they worked better than most other people's (he could see sideways as well as straight ahead, unlike fashion-models with their deep-set eyes). (For an account that sees Socratic irony more negatively, there is a recent on-line article by Michel Narcy, in French but with an English abstract, "Qu'est-ce que l'ironie socratique?")

Soc. Attend now to the questions which I ask him, and observe whether he learns of me or only remembers.
Men. I will.
Soc. Tell me, boy, do you know that a figure like this is a square?
Boy. I do.
Soc. And you know that a square figure has these four lines equal?
Boy. Certainly.
Soc. And these lines which I have drawn through the middle of the square are also equal?
Boy. Yes.
Soc. A square may be of any size?
Boy. Certainly.
Soc. And if one side of the figure be of two feet, and the other side be of two feet, how much will the whole be?
Let me explain: if in one direction the space was of two feet, and in other direction of one foot, the whole would be of two feet taken once?
Boy. Yes.
Soc. But since this side is also of two feet, there are twice two feet?
Boy. There are.
Soc. Then the square is of twice two feet?
Boy. Yes.
Soc. And how many are twice two feet? count and tell me.
Boy. Four, Socrates.
Soc. And might there not be another square twice as large as this, and having like this the lines equal?
Boy. Yes.
Soc. And of how many feet will that be?
Boy. Of eight feet.
Soc. And now try and tell me the length of the line which forms the side of that double square: this is two feet — what will that be?
Boy. Clearly, Socrates, it will be double.
Soc. Do you observe, Meno, that I am not teaching the boy anything, but only asking him questions; and now he fancies that he knows how long a line is necessary in order to produce a figure of eight square feet; does he not?
Men. Yes.
Soc. And does he really know?
Men. Certainly not.
Soc. He only guesses that because the square is double, the line is double.
Men. True.
Soc. Observe him while he recalls the steps in regular order. (To the Boy.) Tell me, boy, do you assert that a double space comes from a double line? Remember that I am not speaking of an oblong, but of a figure equal every way, and twice the size of this — that is to say of eight feet; and I want to know whether you still say that a double square comes from a double line?
Boy. Yes.
Soc. But does not this line become doubled if we add another such line here?
Boy. Certainly.
Soc. And four such lines will make a space containing eight feet?
Boy. Yes.
Soc. Let us describe such a figure: Would you not say that this is the figure of eight feet?
Boy. Yes.
Soc. And are there not these four divisions in the figure, each of which is equal to the figure of four feet?
Boy. True.
Soc. And is not that four times four?
Boy. Certainly.
Soc. And four times is not double?
Boy. No, indeed.
Soc. But how much?
Boy. Four times as much.
Soc. Therefore the double line, boy, has given a space, not twice, but four times as much.
Boy. True.
Soc. Four times four are sixteen — are they not?
Boy. Yes.
Soc. What line would give you a space of eight feet, as this gives one of sixteen feet; — do you see?
Boy. Yes.
Soc. And the space of four feet is made from this half line?
Boy. Yes.
Soc. Good; and is not a space of eight feet twice the size of this, and half the size of the other?
Boy. Certainly.
Soc. Such a space, then, will be made out of a line greater than this one, and less than that one?
Boy. Yes; I think so.
Soc. Very good; I like to hear you say what you think. And now tell me, is not this a line of two feet and that of four?
Boy. Yes.
Soc. Then the line which forms the side of eight feet ought to be more than this line of two feet, and less than the other of four feet?
Boy. It ought.
Soc. Try and see if you can tell me how much it will be.
Boy. Three feet.
Soc. Then if we add a half to this line of two, that will be the line of three. Here are two and there is one; and on the other side, here are two also and there is one; and that makes the figure of which you speak?
Boy. Yes.
Soc. But if there are three feet this way and three feet that way, the whole space will be three times three feet?
Boy. That is evident.
Soc. And how much are three times three feet?
Boy. Nine.
Soc. And how much is the double of four?
Boy. Eight.
Soc. Then the figure of eight is not made out of a line of three?
Boy. No.
Soc. But from what line? — tell me exactly; and if you would rather not reckon, try and show me the line.
Boy. Indeed, Socrates, I do not know.
Soc. Do you see, Meno, what advances he has made in his power of recollection? He did not know at first, and he does not know now, what is the side of a figure of eight feet; but then he thought that he knew, and answered confidently as if he knew, and had no difficulty; now he has a difficulty, and neither knows nor fancies that he knows.
Men. True.
Soc. Is he not better off in knowing his ignorance?
Men. I think that he is.
Soc. If we have made him doubt, and given him the "torpedo's shock," have we done him any harm?
Men. I think not.
Soc. We have certainly, as would seem, assisted him in some degree to the discovery of the truth; and now he will wish to remedy his ignorance, but then he would have been ready to tell all the world again and again that the double space should have a double side.
Men. True.
Soc. But do you suppose that he would ever have enquired into or learned what he fancied that he knew, though he was really ignorant of it, until he had fallen into perplexity under the idea that he did not know, and had desired to know?
Men. I think not, Socrates.
Soc. Then he was the better for the torpedo's touch?
Men. I think so.
Soc. Mark now the farther development. I shall only ask him, and not teach him, and he shall share the enquiry with me; and do you watch and see if you find me telling or explaining anything to him, instead of eliciting his opinion. Tell me, boy, is not this a square of four feet which I have drawn?
Boy. Yes.
Soc. And now I add another square equal to the former one?
Boy. Yes.
Soc. And a third, which is equal to either of them?
Boy. Yes.

Soc. Suppose that we fill up the vacant corner?
Boy. Very good.
Soc. Here, then, there are four equal spaces?
Boy. Yes.
Soc. And how many times larger is this space than this other?
Boy. Four times.
Soc. But it ought to have been twice only, as you will remember.
Boy. True.
Soc. And does not this line, reaching from corner to corner, bisect each of these spaces?

Boy. Yes.
Soc. And are there not here four equal lines which contain this space?
Boy. There are.
Soc. Look and see how much this space is.
Boy. I do not understand.
Soc. Has not each interior line cut off half of the four spaces?
Boy. Yes.
Soc. And how many spaces are there in this section?
Boy. Four.
Soc. And how many in this?
Boy. Two.
Soc. And four is how many times two?
Boy. Twice.
Soc. And this space is of how many feet?
Boy. Of eight feet.
Soc. And from what line do you get this figure?
Boy. From this.
Soc. That is, from the line which extends from corner to corner of the figure of four feet?
Boy. Yes.
Soc. And that is the line which the learned call the diagonal. And if this is the proper name, then you, Meno's slave, are prepared to affirm that the double space is the square of the diagonal?
Boy. Certainly, Socrates.
Soc. What do you say of him, Meno? Were not all these answers given out of his own head?
Men. Yes, they were all his own.
Soc. And yet, as we were just now saying, he did not know?
Men. True.
Soc. But still he had in him those notions of his — had he not?
Men. Yes.
Soc. Then he who does not know may still have true notions of that which he does not know?
Men. He has.
Soc. And at present these notions have just been stirred up in him, as in a dream; but if he were frequently asked the same questions, in different forms, he would know as well as any one at last? [82b-85d]

For another general discussion that starts from this argument but ranges more widely, see Dennis Lomas, "Diagrams in Mathematical Education: A Philosophical Appraisal" and Erick Smith's reply, from the Philosophy of Education Society Yearbook for 1998 — note that the diagram Lomas uses is not what Socrates uses in the Meno proof.