The method, in one worked example 

The procedure has a name in the scholarship, elenchus, meaning examination or refutation, and a shape you can run yourself in about ninety seconds.

It begins with a question of the form what is X, where X is a word the other person uses with authority. In Plato's Laches, two experienced generals are asked what courage is. One answers in the obvious way: courage is standing your ground in the ranks and not running away. It is a good answer. It is what a soldier would say, and both men have earned the right to say it.

Then the questions arrive. What about the cavalry, or the Scythian archers, who fight by retreating and turning back? They are brave, and they run away by design, so holding position cannot be what courage is. Broaden it, then: courage is a kind of endurance. But a man can endure stubbornly in a foolish cause, and we would call that recklessness rather than courage, so endurance alone is not enough either. Add wisdom: courage is wise endurance. Now the trap closes, because the wise thing to endure is determined by knowing what is genuinely good and bad, which turns out to be the definition of every virtue rather than of this one specifically.

The dialogue ends without an answer. Many of them do, and that is not a literary failure. The result is not a definition but the discovery that a competent, decorated, entirely respectable man cannot say what the thing he is famous for actually is. Plato's Socrates keeps insisting that he is in the same position and has nothing to teach, only questions to ask, which is either genuine humility or the most effective rhetorical posture ever devised, and the sources will not settle which.

Two features of the method are easy to miss. The first is that it operates entirely on the other person's own commitments. Socrates supplies no premises of his own. Every contradiction is generated from things his partner has already asserted, which is why the experience is uncomfortable and hard to escape by disagreeing. The second is that it is cooperative in form and adversarial in effect. In front of an audience, being shown that you cannot define the virtue you embody is a public defeat, however politely conducted.

Socrates claimed he took this up because of a puzzle set by an oracle, which he had spent years trying to disprove.