You can read Crito online in English at the Perseus Project and in French at Wikisource.
Socrates is in prison, already condemned; he is waiting because of the current religious celebration, which requires that a ship sail to the island of Delos and back, during which time no one can be executed.
There is also a guard who lets Crito in, although he doesn't seem to be present for the dialogue; he will, however, have a speaking part in Phaedo.
Socrates wakes up and finds Crito sitting with him. He asks him why he is there so early, since it is just before dawn, and why Crito had just sat there in silence rather than awakened him. Crito replies that he did it because Socrates was sleeping peacefully. He has always regarded Socrates as having lived a life that was happy (eudaimonisa), and especially does so now that he bears his misfortune so well.
Socrates replies that at his age it would be absurd to resent dying; Crito responds that this has not stopped other people. Socrates says that this is true and asks again why Crito has come so early.
Crito says that he has heard form a reliable source that the ship sent to Delos is almost at Athens, and will arrive within a day, so that Socrates' execution will be the next day. Socrates replies that that's fine, but he thinks it will not; he has had a dream that suggested that it would actually take another day.
This leads into the discussion, in which Crito tries to convince Socrates to leave the prison: the guard is bribed, there is a ship waiting, and all he has to do is walk out of the door and escape death. But Socrates, of course, refuses, arguing that this would be inappropriate, and the dialogue ends:
CRITO: I have nothing to say, Socrates.
SOCRATES: Let it be then, Crito, and let us act in this way, since this is the way the god is leading us. (54d-e)
Crito has several arguments for Socrates. Interestingly enough, he clearly seems to anticipate that Socrates will not be easily convinced, and so he begins not by any ordinary appeal but by arguing that Socrates should escape for Crito's sake. If he doesn't, everyone will think Crito loved money more than Socrates. Socrates dismisses this -- why should they worry about the opinions of the majority -- but Crito replies that Socrates' own case shows that the majority have the power to inflict the greatest evils. Socrates dismisses this as well; he wishes the majority could inflict the greatest evils, since then they would have the capability for the greatest good (cp. Hippias Minor).
Crito asks if Socrates is worried about what would happen to the people he'd be leaving behind, and Socrates says he is, so Crito argues that they will be fine. He then returns to his argument: by staying, Socrates is not being just, and he is betraying his family, and he is leaving his friends in a shameful position. Socrates responds that they should examine the matter, since "I am the kind of man who listens only to the argument that on reflection seems best to me" (46b). They both agree that people should only value the good opinions of wise man, not any other kind of opinion. "We should not then think so much of what the majority will say about us, but what he will say who understands justice and injustice, the one, that is, and the truth itself" (48a). But the just stays the same regardless of whether one is put to death or not.
They then both agree that it is always wrong to mistreat others, even if one is mistreated oneself, and that one should fulfill one's agreements. This leads to the most famous section of the dialogue, the Speech of the Laws, in which Socrates imagines the Laws of Athens themselves coming to him and confronting him.
The Laws argue that the city depends on the verdicts of the courts having force; without them the Laws themselves fail. But Socrates as an Athenian is obligated to the Laws of Athens, since they made possible the marriage of his parents and his birth and his education. He owes to them an even great debt of piety than he owes to his parents. And if Socrates didn't like the Laws, he was always able to leave, no harm done; but those who remain in Athens are thereby agreeing either to do what the Laws of Athens say or to 'persuade' them (i.e., change them by lawful means). Socrates has very definitely stayed, and lived out his life, under the Laws of Athens, and even insisted in his defense speech that he would prefer death to exile (cp. Apology).
Moreover, the Laws argue, he will leave his friends open to danger by leaving, and if he goes to Thebes or Megara ("both are well governed" (53b)), people there would be right if they regarded him as a danger, since he is so willing to disregard laws when convenient for him. He would have to go out among the barbarians, and what would he do then? And how absurd it would be to go through such lengths given that he certainly does not have a very long life ahead of him, anyway! As for his children, his friends will educate them as much if he goes to the underworld as they will if he goes to Thessaly. Thus, the Laws say,
Do not value either your children or your life or anything else more than goodness, in order that when you arrive in Hades you may have all this as your defense before the rulers there. (54b)
And if Socrates is killed, he will have been wronged by men, not by the Laws.
* Diogenes Laertius notes some interesting gossip about this dialogue, in his Life of Plato. He says that Plato hated Aristippus, and was antagonistic to Aeschines because of his good relations with Aristippus: "And Idomeneus says, that the speech which Plato attributes to Crito in the prison, when he counselled Socrates to make his escape, was really delivered by Aeschines, but that Plato attributed it to Crito because of his dislike to the other."
As with most of the gossip of Diogenes Laertius, we don't know how much there is to it. But it is interesting that there was the idea that it was really Aeschines, not Crito, who discussed this matter with Socrates, and it raises an interesting question: Is there anything Plato can get out of attributing this discussion to Crito rather than to another student of Socrates?
I think this gives us interesting food for thought, because the discussion is consistent with how Plato depicts Crito elsewhere (firm supporter of Socrates, regards philosophy as a good in an abstract way, yet is somewhat detached from the practice of philosophy), and it's perhaps not insignificant that by this time Crito is one of Socrates' oldest living friends -- perhaps his oldest living friend, since Chaerephon has already died. One way to read the dialogue is as Socrates reminding his old friend of what he and Socrates have always held to be important.
* The force of the Speech of the Laws is easy for us to miss, I think, because we don't have the filial piety of ancient Greece. What the Laws are arguing is that Socrates owes to the Laws of Athens an obligation even greater than that which he owes to his parents, and of the same kind; thus all the cultural backing behind proper behavior to parents should also be applied to the Laws. This is a powerful and very forceful argument in a culture like ancient Greece in which piety towards one's parents was a major feature of common decency, and failures of such piety terribly shocking (cp. Socrates' response to Euthyphro prosecuting his own father for impiety). (It would continue to be a forceful statement in the Roman empire, for the same reason, and if it had ever made it to China, it would have been a very forceful statement there.) There is also, of course, the fact that Socrates was tried for impiety; and, ironically, if he owes the Laws piety, by doing something harmful to them he would be doing something impious for the first time in his life.
* Due to Grote, it is often said that the argument of the Laws at 51b-c is inconsistent the passage in the Apology where Socrates said that even if the men of Athens gave him life on the condition that he not philosophize, he would disobey them. But it should be noted (a) in the Apology the point is that the god's authority trumps human authority, and that he would be obeying the god; (b) the Laws here do not argue that one should obey one's city without question, but that one should either obey it or "persuade it as to the nature of justice" (51c). The latter, of course, involves philosophizing.
* The flutes of the Corybants, mentioned by Socrates, refers to an ecstatic cult devoted to the goddess Cybele. The expression means that Socrates, inspired by the words of the Laws, is made heedless of anything else.
Quotations from Crito are from G. M. A. Grube's translation in Plato, Complete Works, Cooper & Hutchinson, eds. pp. 37-48.