The fighting in this game is extremely fast and fluid. Matches are usually 2 vs 2/3 vs 3 with special moves going off left and right. It can be chaotic but I never felt overwhelmed. The camera is bothersome at times in close quarters, though the majority of arenas are vast outdoor environments.
Time Patrol is the game's story mode which has you fighting alongside the z-warriors during different sagas. Your created character travels through time aiding in familiar battles we've all come to know and love. I won't detail the reasons behind your actions for spoiler purposes.
Side missions are available in the form of Parallel Quests. These missions can be tackled solo or with a single friend and are vital to improving your character. Equipment, items, money, skills and XP are all rewarded upon completing these quests. More PQ's open up the further you progress in TP.
When not playing TP or PQ, you can wander around the Time Nest for training opportunities, markets to shop at, or just interact with other gamers. Before jumping into the game you can select whether you want your TN lobby to be offline or online.
Specials moves can be purchased, though I believe some require training before they're available. I've earned and purchased minor characters (Recoome, Raditz, Nappa, etc.) moves via mission completions, but the main characters like Vegeta and Krillin can be found in the Time Nest for training. Training with a master will unlock their specific moves like the destructo-disc and galick gun. So far I've only seen 3 trainers, but I'm sure more will show up later.
There is also an online battle mode, but I haven't spent much time on it.
I highly recommend this game to all DBZ fans and will gladly answer any questions you guys have.