There are three major aspects to
Dragon Ball Z: Budokai 2, unlocking characters, earning Zini (DBZ money) and buying skills. These areas are split up among three modes, Dragon World, World Tournament and Edit Skills.
In the World Tournament Mode, you fight through the ranks of various tournaments. The size of the tournament depends on the level you set it to. The three levels are Novice, Adept and Advanced. At first the only one available is Novice, where you will be in a tourney with seven other characters. After you have unlocked enough characters to fill the rosters of the other two tournaments (16 for Adept and all 29 for Advanced), they will be available for purchase in the Skill Shop.
You go through the tournaments in order to earn Zeni. You only get this money if you are the Runner-up or the Champion. The more advanced the tournament, the more Zeni you will get. This comes in handy when you go to the Skill Shop in the Edit Skills option. Here you will be able to purchase capsules (skills) for any of the unlocked characters. This is also where you can add those skills to your characters. Also carried over from the first Budokai is the ability to trade skills with other players; all it takes is the other player's memory card.
And now for the meat of Budokai 2, Dragon World. This replaces the previous game's Story Mode. Some of the problems I had with the Story Mode of the last game were how quick it was to play through, how little time was spent in each fight and how brief the cutscenes were. In Dragon World, things are a lot different. The story spans the entire Dragon Ball Z story arc, but does it in a far more liberal way. The story portrayed in Budokai 2 only roughly follows the show, and normally I would have a problem with that, but when you consider what was done with the story in the last game, I can forgive this easily.
Dragon World is basically a map where you will move about going after the baddies and keeping the world safe. You will play (mainly) as Goku, but in each stage (nine in all) you can select one or two other Z-fighters to control. Because of this map system, there is an element of strategy that needs to be addressed before each movement and battle, especially if you are trying to pair up a particular fight in order to unlock a character.
Across the map there are various items that will increase your attack power or armor, but be careful, because if one of the enemies reaches one of these items, then they will get the boost. Also found in each map is at least one Dragon Ball. If you collect all seven and complete the Dragon World story, then you can ask the dragon for one wish. In order to unlock all of the characters, you must complete this task. Another aspect about the map that forces you to consider your moves is the Battle Conditions that accompany many of the locations. These range from fighting with decreasing health or Ki (the energy you use for your attacks), or starting with half your health, as well as a few more conditions. Thankfully, you aren't the only one who has to follow these conditions. There were a couple of instances that I would not have made it past an enemy if it weren't for little complications.
It is in this mode where you unlock most of the new characters. This is an interesting aspect because unlike most fighting games, you don't just get the character because you beat him or her; you have to beat him or her with a specific character. This is good for fans of the show because which character you need is based off of the relationships from the series. For instance, to unlock Android 18, you need to defeat her with Krillin. Other matches that will yield new characters are Cell and Gohan, Majin Buu and Hercule, Goku and Frieza, and Vegeta and Captain Giynu. There are a total of 29 characters, and you only start off with 8 so there is plenty of room to grow in Budokai 2.
Before the story is over you will face Cell and Frieza many times (many, many times). You will also go up against Majin Buu, Super Buu and Kid Buu. Unfortunately you cannot unlock the Buus the same way you can the others. An interesting aspect is that the only way to unlock all of the characters (and thus open the Adept Tournament Mode) is to play through the Dragon World several times. This is because sometimes beating a character with a couple of different good guys will allow you to unlock other characters. Because of this, there is a lot of replayability in this game, unlike the Story Mode of the first Budokai.
There is also Training Mode and Duel Mode. Duel Mode allows you to face another person head-to-head, while Training Mode lets you to try out the various abilities against an opponent (either standing still, or fighting back) without the fear of being KO'ed.
As far as the battles themselves are concerned, they are pretty much the same as before. They tend to be quick and full of flashy moves, though there are a few changes that should be mentioned. The major change in the matches is that sometimes when your opponent uses some massive attack against you, you will have the ability to either avoid the attack completely or make it cause less damage -- which it is depends on which move they use. For moves like the Zanku Fist, while the aggressor flies toward you, a bar comes up asking for input from both players. If they are the same button, then the attacked will dodge out of the way.
When the player uses an ultimate move like Spirit Bomb, you will both have to move the Left Analog sticks as fast as you can in order to force the power onto the other player -- this results in a tug-of-war effect (though I have yet to move the bar onto the other player's side). These changes aren't only to help the attacked. Some moves allow the attacker to spin his stick as fast as possible in order to increase the amount of damage the blasts do. Fill it up and you will release an extra blast.