The two main forms of PVP are Battlegrounds and the Arena. (There's also world PVP, but this only occurs if you're on a PVP server. It can be a lot of fun and gets the blood pumpin'. But it can also be painful and annoying.)
Battlegrounds you'll be on a team anywhere from 10-40 players depending on the specific BG you join versus an (hopefully) equal amount of players. Different battlegrounds have different objectives. Capture the Flag, Control the Node, both at once, "Assault" type maps, etc.
Arena you'll be on a team of 2, 3 or 5 of your choosing, so it'll usually be people you know. During a match you'll be in a small arena versus an equal number of opponents and you just fight until you win (Or lose). The arena rating system makes it so that the better your team does, the more awesome PVP gear you gain access to. And if you're really good, you'll get a special title and mount.
Raids you can either do with either 10 or 25 people, the latter supposedly being harder and giving better rewards. There are many different raids already as well as a new one that is coming with the patch. It takes teamwork and dedication to beat the strongest raids. Then you can do it in your sleep and get gr8 epicz. lawl. (Results may vary)
So that's the very general basics.