I'll try to get a scan and upload it tomorrow. These rules are written word for word almost.
But here are the basics.
Gameplay is the same. Youngest goes first etc etc etc.

Picture taken from TeamBIB.
Battle Gear:Each Battle Gear comes with a reference card. These cards aren't put in your used or unused pile. They are kept nearby so you can see any special rules it might have.
Bakugan Battle Gear are played during a battle (from your Unused pile). Place your Bakugan Battle Gear on the back of your Bakugan to open it.Bakugan Battle Gear may also be opened on a Gate Card. Add the G-Power revealed on the inside of your Bakugan Battle Gear to your battling Bakugan. If your Bakugan's Attribute matches either of the attributes on your reference card, then you get that ability as well.
Or, if your Bakugan Battle Gear matches the color of the Gate(Bronze, Silver or Copper)*, you choose any one ability on the reference card to use in this battle.
Bakugan Trap and Bakugan Battle Gear move like regular Bakugan. At the end of a battle, they move to your used pile. When you have no Bakugan to roll, all of your Bakugan, Bakugan Trap, and GEAR move to your unused pile.
Each player may include a total of 2 Bakugan Trap and/or Bakugan Battle Gear in a game. (4 in a Big Game).
*Note that was not a typo on my part but thats how it reads on the official rules.
Power Level:The Power Level for the game is the total number of Gate cards in all player's used piles. If you see it on an Ability card, it means that you can't play that card until the Power Level of the game is at least equal to the Power Level listed on the card.
Special Evolution:Note: Each Special Evolution Bakugan comes with a reference card. These cards aren't put in your used or unused pile. They are kept nearby so you can see any special rules it might have.
Special Evolution Bakugan don't start the game in a player's unused pile. To get a Special Evolution Bakugan into the game you must meet two conditions (found on the reference card). First the Power Level of the game must be at least equal to the Power Level of the card. Second, you must have a Bakugan in your used or unused pile from which your Bakugan evolves (also shown on the reference card). If you meet both conditions, you may skip your turn and swap the Special Evolution Bakugan for the one that it evolves from.