You'll find master characters around the city and more appear as you complete the various story arcs. It's always a significant character and they'll have a pink marker over their heads so you can't miss them. At the start of the game, you have Piccolo, Kuririn, Tenshinhan and Yamcha available, with more appearing as you complete more story arcs. You won't be able to complete your lessons with some until reaching a high enough rank at the academy (where Orange Star High School is, talk to Elder Boss Kaioshin to do the necessary exam battle). Another thing worth noting about the exams is that by completing each one with a Z rank, you unlock the Super Class exam and get the Potential Unleashed transformation by completing it, which is the most useful transformation for story and parallel quests (or at least it was. I've heard they buffed the Pure Majin form recently).