A Quick Battle can be either a single vs. CPU match or a series of elimination matches called Team Battle. In vs. CPU it is simply a single match against a computer opponent. In Team Battle, you choose up to eight characters to compete against the computer in a series of matches. If the character loses a match, they are eliminated, and the next character you chose competes against the character that eliminated the previous character.
This is the same as the arcade mode in most previous Tekken titles (and the PS3 version), in that you fight a series of characters and the game plays bits of the character's storyline. After a small number of battles you face the final boss, and hopefully complete that character's story arc.
This is similar to Ghost Mode on the PS3. You compete against a series of Ghosts, computer opponents with differing attack styles and strengths, which continues as long as you wish to continue playing. The ranks of the ghosts will change as your character's rank changes, and you can select from 3 opponents (or to exit Arcade Battle) after defeating an opponent.
You can choose between vs. and Team Battle to compete against other players (also playing the PSP version of the game). The game also supports Game Sharing, so that two players can compete in a vs. match with only a single copy of the game.
Tekken Dojo allows you to compete for rankings in a series of Dojos, which in turn have a series of leagues and tournaments in which to compete. The basic premise is to enter League Matches to increase your rank until the Ranking Tournament becomes available, and then compete in the Ranking Tournament to be ranked number one in that particular dojo. More dojos will become available as you increase your overall ranking and standing within a particular dojo.
A set of minigames in which you compete for the highest score.
Practice with any of the characters. Move lists and demonstrations of the moves can be viewed here.
Bonus Games such as Tekken Bowl (a bowling minigame) can be unlocked through playing ranked matches (ie. Tekken Dojo, Story Battle, Arcade Battle, and Network Vs. matches).