If your only goal is to make it through the two PVP games for the Wrathion quest line and you never intend to PVP again, the key is to play when the Alliance tends to win more, which is generally during the day on weekdays (I'm not sure why, this is an empirical observation). If you can't do that, just keep going back and trying, eventually the Alliance will get a weaker Horde group. It took me 5 tries to get the 2 BG wins I needed, for example, but this was during the early evenings.
I'm certainly not a PVP expert, but my perspective is someone who used to PVP some (arena teams back in season 2-3) and is now strictly PVE.
If you really want to get better at PVP:
1) Read the basic guides on specs and gear; you'll want your second spec to be PVP oriented. Be prepared to put some money and effort (farming for Honor, for example) into gearing up.
A few crafted pieces plus drops from the Sha will likely form your initial gear set; at first, PVE gear may be better if you're a raider, but you'll have to judge when to swap over to PVP gear.
2) Read up a guide on PVP playstyle; playing against humans is very different than the computer. A lot of PVP revolves around CC and interrupts. You're not interested in conserving resources (generally), but piling on (burst damage) and getting someone down. Be prepared to die a lot.
I would suggest doing regular battlegrounds first, learning how to play your character and the particular BG strategies (e.g. flag capping and defending, or the blind rush that Alterac Valley has degenerated into) while earning Honor points for some gear. Serious players are into arena and rated BGs and you'll likely get crushed in those if you just throw together an inexperienced team.
You'll also want to figure out your preferred role and play style, which will depend on your class and spec; mages used to be ultra-squishy (less so now), so I tended to do larger BGs (like AV, Baradin Hold, etc) since it was easier to blend into a crowd to stay alive rather than be forced into a one-on-one, which mages tended to not fare well in. Some specs are better at one-on-one and thus may want smaller groups.
If you want more specific advice, I'm sure someone around here can probably help...