The book, like Alcibiades, with which it has some interesting parallels, has often been regarded as an introduction to the Platonic dialogues.
You can read Theages online at the Perseus Project, as well as in French at Wikisource.
(in order of appearance)
Demodocus is mentioned in passing in the Apology, where he is said to have two sons, Paralus and Theages. In this dialogue he is said to be a farmer or country gentleman.
Theages is referred to in the Republic, where Socrates says in passing that many things conspired to divert Theages from philosophy. According to the Apology, Theages dies fairly young.
The Plot and The Thought
Demodocus opens the dialogue accosting Socrates and asking for his advice in educating his son, Theages, who is demanding that Demodocus hire a Sophist, who will make him wise (sophon). Socrates suggests that the best way to start is to make sure they know exactly what Theages is wanting, so the dialogue moves from being advice to Demodocus to being a discussion with Theages. He begins by asking whom Theages considers wise or knowledgeable. Then Socrates goes through different kinds of wisdom -- that of the pilot, that of the charioteer, that of the doctor, and so forth. Theages isn't interested in these kinds of wisdom, though; he wants the kind of wisdom that directs all these lesser kinds of wisdom; and, in particular, the kind of wisdom that directs them by ruling them in a city.
As Socrates gets Theages to admit, though, this means that he wants the wisdom or knowledge of the tyrant, and is asking his father to pay to have him associate with someone who has this tyrant's knowledge. He turns to Demodocus and begins a discussion of what people might be suitable teachers. Theages accuses him of making fun of him: he and anyone else would want to rule over people, but "not by violence, the way tyrants do," but only over people who would submit voluntarily, the way men rule who are of good repute in the city: people like Themistocles, Pericles, and Cimon.
If Theages wants political wisdom, then it seems he must associate with politicians. But Theages notes that the children of politicians, who obviously do associate with politicians, seem to be no better than the children of anyone else. This, of course, creates a puzzle: how do you learn political wisdom if you have no respect for politicians? Socrates suggests that if this is so, perhaps it is better to save money and have Theages associate with someone who doesn't charge for it. Theages agrees and suggests Socrates himself. Demodocus thinks this is a great idea.
Socrates denies that he's a reasonable choice; Demodocus himself, who is respected in the city, would be a better choice, or even, despite the cost, teachers like Prodicus, Gorgias, or Polus. Socrates himself knows only one subject well: love, "although on this subject, I'm thought to be amazing, better than anyone else, past or present".
Theages moans to his father that Socrates is only playing games with them; he knows several people who were nothing before associating with Socrates and have since become much better people. If Socrates agreed to take him on, Theages could become like them. Socrates insists that Theages does not understand:
There's a certain spiritual thing which, by divine dispensation, has been with me from childhood. It's a voice that, when it comes, always signals me to turn away from what I'm about to do, but never prescribes anything. And if some of my friends consults with me and the voice comes, it's the same:it prohibits him and won't allow him to act. (128d)
Socrates gives a number of examples of this, then continues:
I've told you all these things because this spiritual thing has absolute power in my dealings with those who associate with me. O the one hand, it opposes many, and it's impossible for them to be helped by associating with me, so I can't associate with them. On the other hand, it does not prevent my associating with many others, but it is of no help to them. Those whose association with me the power of the spiritual thing assists, however--these are the ones you've noticed, for they make rapid progress right away. And of these, again, who make progress, some are helped in a secure and permanent way, whereas many make wonderful progress as long as they're with me, but when they go away from me they're again no different from anyone else. (129e-130a)
Thus Socrates has no control over who benefits from his teaching and how. This is an interesting move, because given how Socrates tends to talk about teaching, both here and elsewhere, it means that when people learn from him, he is nonetheless in some real sense not their teacher.
Theages suggests that they test it by associating with each other and seeing how it goes. Demodocus agrees, and Scorates ends the dialogue by relenting.
* Theages' name has the word 'god' as its root; Socrates highlights this by mentioning that it's a godly name at the beginning of the dialogue. This no doubt connects with the subject matter.
* Themistocles was one of the great generals and leaders of the Athenians during the Persian War. He became archon in 493 and convinced the Athenians to engage in a massive expansion of their naval power -- indeed, through the course of his career he convinced the Athenians to engage in several such massive expansions of naval power. Due to his arrogance, he intensified tensions between Athens and Sparta, and eventually annoyed enough people that he was forced to flee to Argos, from which he was again forced to flee by the Spartans. He went to Persia and became a governor there. Cimon was another Athenian general who made a name during the Persian War; he was pro-Sparta and led the opposition to Pericles. Pericles himself, of course, was the dominant leader of Athens through much of the Peloponnesian War. Pericles at one point had Cimon tried for treason (Cimon was acquitted). The three would have been considered great statesmen by the Athenians; it is a consistent theme with Socrates throughout the dialogues, however, that much of their greatness was illusory.
* It's possible that the explicit mentions of Gorgias and Polus are intended to link this dialogue to Gorgias, in which Gorgias and Polus are both characters.
* Socrates' daimonion is well attested -- it is mentioned several times by both Plato and Xenophon. They differ, however, in that Xenophon says the daimonion both prohibited and prescribed, whereas Plato insists that it only prescribed; the author of this dialogue, if not Plato, follows Plato.
A daemon or daimon was an intermediate spirit between gods and men; they were often held to carry sacrifices and prayers to the gods (Plato explicitly says this in the Symposium). As intermediate entities, the lines between them and human spirits, on the one side, and gods, on the other, are not always bright and clear. Socrates' divine voice or inner oracle is a daimonion, which has a diminutive ending and might be translated as 'daemonling' or 'daemon-like something'. Plato elsewhere does not conflate daimonion and daemon, but treats them as if different, with the daimonion being an impersonal sign, not a personal being; the two seem conflated here, which is a major reason why many Plato scholars take the dialogue to be spurious or at least doubtful.
* It's easy to miss, but there are three different approaches to education in this dialogue. Demodocus thinks of education along the lines of cultivation; this is exactly how he characterizes at the beginning. He is in tension with his son because his son is not satisfied with how Demodocus thinks things should be done: he wants to be taught at a school, essentially, and have his father pay for this teacher. Demodocus regards this as extremely dangerous, and worries that it will corrupt the boy. Socrates provides an alternative to both: his teaching is neither mere cultivation nor an artificial system. It differs from both in that it cannot be reduced to the hard work or expertise of the teacher; control over the result does not belong to Socrates, but to the god. Socrates explicitly presents it as a third alternative: when he suggests that there are better options, his two options are Demodocus and Theages' alternative of the Sophists or artifical teachers, and he distinguishes himself from both. But since his third option avoids the danger of corruption that had Demodocus worried and opened the possibility of wisdom, which Theages wanted, it is able to serve as something they can both accept.
* It would be interesting to compare this dialogue with Aristophanes' The Clouds, which mocks Socrates.
In his translation of Theages into French, Victor Cousin has an interesting note, which I translate here:
The purpose of this little dialogue, or at least the only serious point that we can see, is the important distinction between Socrates' manner of teaching and that of the Sophists. It was not by regular courses and lessons, like the sophists, nor books, like modern [teachers], that Socrates had acquired so much influence over the minds of his fellow citizens, and spread around him enlightenment and instruction. Instead of the often sterile apparatus of school-knowledge, artificial and mannered, all of his art consisted in putting those who associated with him in more or less intimate contact with his soul, to fertilize and develop them by sympathetic charm. Where sympathy was lacking, Socrates himself could do nothing. This mysterious instinct, whose source lies in causes beyond the human will, the bond that unites hearts without their knowing and often despite them, the rapport at once irresistible and inexplicable, was necessary for Socrates to act and be useful, and friendship was for him the condition and instrument of all great and noble influence. So, to speak truly, he had no students, only young people who clung to him. He talked and lived with them; this was his education. This teaching was by chance, on the promenade, at gyms, in public places, always and everywhere and in everything improvised, naive, varied, full of life. Perhaps he did not leave in their minds this or that determinate system; but he inculcated in them excellent habits, and in every sense opened thought along healthy and original lines. Socrates formed no particular school; better than this, he created an intellectual movement which, by closer and closer communion, embraced bit by bit the whole of Greece, and through Greece all mankind.
Quotations from Nicholas D. Smith's translation in Plato, Complete Works, Cooper & Hutchinson, eds., pp. 627-638.