Yes, yes we do. We have numerous handbooks and writings in Greek that describe the theory of rhetoric, as well as the kinds of instructional courses that were utilised. We also have the equivalent of textbooks, thinks like the Progymnasmata, which are essentially exercises in composition.

Generally a well-educated child would be trained first in an equivalent to elementary school, by a grammatistes, through rote memorisation of letters, sounds of syllables, and then reading words and sentences, on to memorisation of important literary passages.

From here, it was on to grammatical study. We have Dionysius Thrax's Grammar, which was use from around 100BC onwards as a textbook on Greek grammar, for a good 1500 years. This kind of study would involve: reading aloud, identification and analysis of poetic metre, identification of figures of speech, commentary on rare and historically significant words, conjugating and declining of word forms, and literary criticism of literary works.

More advanced study was 'rhetoric' proper.. This involved studying methods and techniques of argument and persuasion. Students would study classic texts, as well as give speeches/papers arguing for various positions, sometimes theoretical, sometimes speculative history. Further study might be done in the Philosophical schools.

The person to read is George Kennedy, who made a career out of writing on Rhetoric in the ancient world. I would recommend his A new History of Classical Rhetoric

Feel free to ask further questions, this is right up one of my alleys.