All you do is queue up for one of the battlegrounds and you'll be grouped up with the needed amount of other people.
Sadly, most of them are retarded.
The positive thing about that is that your inexperience wont show
And I'll add a small explanation of the BG's here.
I know thatthat is what I found hardest about my first BG's.. no clue what the goal was.
Alterac Valley: 40 vs 40 kill the other side's boss.
Best you can do is follow the group and help kill the mini boss, capture towers and kill the big boss the first couple times until you understand it all.
Arathi Basin: 15 vs 15 capture and hold bases.
5 bases, your team gets points for holding them, first team to 2000 points wins.
Eye of the Storm: combination of capturing and holding bases and capturing the flag.
4 towers and 1 flag, bringing the flag to a tower held by your team gives points, holding towers give points.
Once again a race to 2000 points.
Warsong Gulch: 10 vs 10 capture the flag, first team to capture 3 flags wins.
You cant capture the flag when the other side has your flag.
You get rewarded honour points for killing members of the other team and the whole team gets bonus honour for things like getting a certain amount of points, capturing a flag, destroying a tower etc.
You also get 1 or 3 marks from that specific battleground. (1 for loss, 3 for win obviously)
And for when you're lvl 70 (or more likely 80)
Arena: 2v2, 3v3 or 5v5 deathmatch.
you enter with your own team (so it's not ally vs horde as in BG's) and fight for a rating.
winning adds to that rating, losing costs you rating.
the amount differs based on the difference in rating between the teams.
you gain arena points every week based on your rating.
For more (much much more) details you can check out
ArenaJunkies