I'll fill you in as best as I can...
I'm sure you've played Pokemon Stadium. Where you basically used pre-set Pokemon and Pokemon from your R/B/Y games to battle CPU's. Basically, not much as changed since Stadium to Battle Revolution. You basically battle individual colosseums and work your way up to the top. With each stadium you clear (there are certain criteria you must meet) you will be able to access that stadium during WiFi battles. You can use crappy pre-set battle passes, or download all of your Pokemon from your Diamond/Pearl game to a storage box that the game provides you with. From there you can make whatever team you desire with the Pokemon you own.
What else is there...
You can customize your trainer via PokeCoupons that you earn by battling the colosseums... you can also change what your trainer says when they throw out or return a Pokemon. (doesn't show up online though, for obvious reasons)
Which brings me to my next point, the online...
Basically, you bring a team of six Pokemon with you to the WiFi corner...thing...or whatever you wanna call it. Then you select one of the colosseums you unlocked in single player mode. From there, you wait a moment or two and eventually the game will match you up with a random person, and randomly pick a stage that you and your opponent chose. (I haven't seen many n00bs around lately, so you're gonna get some good battles going, trust me.) The only gripe is, before the battle you get to see which six Pokemon you and your opponent selected, then you choose three Pokemon that best counter the other's team. 3v3's aren't as fun as 6v6 battles, but it would take FOREVER to do 6v6's every single battle. So Nintendo sort of made a good call in that aspect. Also, you can exchange friend codes with your friends or people on this forum and battle 6v6's. The online is the most redeeming part of the game, the single player is kinda boring.
Well, that about sums everything up. Hope you enjoy the game! See you online maybe sometime. xD