You can learn almost all of these concepts by going through the manual or the training section of the practice mode, however, for sake of completion well go over the basics here.
Rushing: Forward, hold Forward
Energy blast: E
Nullify: When one non-special move has certain properties that make it "beat out" other normal moves (moves like Back+P+K, which all characters have).
Bursting: Perform a nullify against an opponents nullify, which will launch you into a masher-friendly combo stage.
Back dash: Back, hold Back
Side stepping: Guard+Up or Guard+Down
Energy fill: While holding G -- Back, Back
Energy deflect: Hit G right before a basic energy blast hits your character. Hitting G early in the collision will deflect the projectile off to the side where hitting G in the later frames will send the projectile directly back to the opponent.
Flip Out (AKA Fall break): When your lifeless body is about to smack the ground, hit Back, Back+G
The harsh reality of Budokai 2s fighting engine is that everything is very restricted in comparison to other fighters. This is especially true in two major areas: immediately accessible moves and height variation of said moves. The majority of the move list available to each character is buried within the strict chain combo system (if you want a specific punch or kick, you are forced to run through a specific chain combo otherwise you are stuck with the basics). The move list, while having differing height variations, doesnt end up meaning much since your opponent blocks every attack the same way (holding guard will block every normal attack regardless of how it mixes up height variety).
The combo system in Budokai 2 exists in a very controlled environment. Combos are literally already laid out for you so that simply mashing on the punch, kick or a combination of the two will dial out a combo for you. The non-existence of height variation and limitations on basically accessible moves makes breaking out of these canned routines very difficult. As of right now, there isnt much you can do for ground based, head to head combos that will allow you to "cancel" one scripted attack string to start another.
Juggles are probably the single element in combos that do allow for breaking out of the scripted routines of the ground chains and open a window for some originality on the players part. When you perform a combo that ends with your opponent popped up into the air (not to be confused with slamming him/her up into a higher plane), you can then perform a second combo that will continue to juggle the opponents body. For those who love playing around with the possibility of long combos, this is probably your only chance to drop out of some combo strings and perform a third or even fourth set of canned combos.
Some things to keep aware of when practicing juggles is that once the body hits the floor, the opponent can flip out/break their fall and block any additional hits. Bouncing the body back up for additional hits is still possible, but if the opponent flips out then the combo is over (infinite combos would, otherwise, run rampant throughout Budokai 2 without the flip out option).
Another element you are fighting against is gravity. The more you wail on the opponents airborne body, the more it wants to land on the ground. Keeping the body afloat indefinitely, even with moves that should re-pop the body up, is very difficult after the first two combo strings.
Attacking an opponent while on the ground is tricky in Budokai 2, especially because of the lack of any real height variation system and the fact that moves that do, technically, hit low may be hidden inside a combo string for some characters. If accessing a normal move isnt a possibility, an energy blast can hit the opponent (as long as you are two to three body lengths away). Some special energy projectiles can also hit a grounded opponent, but will do less damage than if it was performed on a standing target and will more than likely knock the character back on his feet.
Combos into Combos
As mentioned in the juggles section (which might need a little bit more explanation here), it is possible to "drop out" of one combo and into another in Budokai 2. Because there is no canceling of moves in the traditional sense in this game (such as Soul Calibur II or Street Fighter II where you cancel the animation of one move into another), you literally have to stop entering the commands for one combo, then start up another one at the moment the frames from the first combo complete.
As an example, try this in practice mode with Super Buu (try choosing Dabura or Android 16 as a target): K, K, K, Now wait for the moment when the animation is about to end for his back kick, then quickly enter K, K, K. You should have now juggled the opponents body with two combos, setting him up for a third combo, by "dropping out" of the first canned combo.
As of right now, this is only effective for juggling or bouncing your opponents body. Straight up ground based combos in Budokai 2 do not allow for enough hit stun until the very end of the attack string to simply drop out and restart another combo (and usually by the end they are either knocked away, on the ground, or popped up into the air for a juggle).