Since nobody picked this up yet, I will attempt a partial answer. Yes, there most definitely were a defense and a prosecution side. One big difference from what we see today is that the roles were taken by well trained and educated amateurs, rather than paid professionals: often senators, or former holders of public office.

I do not know of full records of a trial, but the sizeable corpus of Cicero's orations includes various judicial speeches, both as a defense attorney (Pro Archia poeta, Pro Roscio Amerino etc.) and as a prosecutor (In Verrem). Any reading guide to Cicero would give you summaries of the speech themselves. I may suggest:

- James M. May. Brill's Companion to Cicero Oratory and Rhetoric (2002, Brill Academic Publishers).