Well, aside from a truly unimaginably large amount of ancient textual evidence, a great deal of it written very soon after his death by people who were intimately acquainted with him (eg, Plato and Xenophon), there was a play written about him during his life (Aristophanes' The Clouds and an ostracon bearing his name.

I've written up a fairly detailed list of early sources here.

I feel I'd better point out that the ostrakon that /u/Tiako mentions doesn't have anything to do with Socrates the philosopher; there was more than one person of that name. The ostrakon names Socrates of Anagyrous (Socrates the philosopher came from Alopeke), who was a general in the Samian War along with Pericles, in 440/39 BCE. Socrates the philosopher would have been a decade or two younger.