If you want to learn more about Cicero's advice on debating, I suggest How To Win An Argument - a collection of Cicero’s writing on argumentation and oratory. The book details his advice on persuasive speaking, building arguments, convincing audiences, and winning debates. The book, while recommended, is only a selection of Cicero’s writing, so I also suggest the original texts.
This post succinctly highlights 5 of Cicero's most important pieces of advice on debate and rhetoric: