Are there any sources from antiquity about the study and teaching of foreign languages?

The closest we have that I know of (and it’s really not very close at all) are the Pseudo-Dosithean Hermeneumata. They’re a third century AD Berlitz phrasebook of Greek and Latin. Nothing about language teaching methodology, and of course not much of a language teaching methodology is on display anyway.

I did find the following exchange in the Berlitz funny though:

bibliotheca Augustana

Colloquium Harleianum:

23. Isn’t that Lucius who’s got my silver coins? Here he is. Then I’ll go and say hello to him. Hail, householder! Am I still not going to get back what you’ve owed me for so long? What are you talking about? You’re crazy. I lent you silver, and you call me crazy? You thief, don’t you know who I am? Why don’t you go look for whoever you made a loan to; I don’t owe you anything. You swear that to me. I’ll swear wherever you want me to; let’s go. Swear in the temple. By the God over here, you did not lend me a thing. Well, fair enough; it’s no good to doubt the word of a free man and householder.

24. And this animal-fighter is making fun of me? Let me go, and I’ll smash his teeth in. Yeah, well I’ll poke your eyes out. I can see what you would do to me. I’ll have you sent to jail, where you deserve to grow old. You’re making fun of me, you prison-guard. I don’t care what you do. You have a friend, and you’ll find one in me. Well said. OK, I forgive you.

… I dunno, maybe the Romans were onto something with their language teaching.