This is a question I have been asked a lot, and while it is possible to pvp with other members of your faction, it is incredibly difficult. Still, if you really want to battle light on light or dark on dark action, here is my guide to making it happen:
1.) Pick a time of the day where there isn't a lot of other people in your faction cooping. This is because the more people there are in the coop queue, the more difficult it will be to get a pvp instead of a coop match while in the Guild Wars queue.
2.) make sure that both you and your pvp mate are both in a guild (but not in the same guild). Your guild cannot be allied with or have a non-aggression pact with their guild either.
3.) Both of you must enter your respective Guild War queues and be within tier and AP range of each other like with a normal PvP. The Guild War queue will put you in both the coop and pvp queues, meaning at this point you could either get a coop or a pvp.
4.) At this point it is useful to have open kong chat. If you match you can /w them "match" and vice-versa to tell whether you got in the same game or not. Still, you could end up in coop.
5.) watch the coop queue, and make sure before matching the queue says "2" (this number is actually you and the person you are trying to PvP). If there is any more than that, a coop match is almost guaranteed, even if you match with the other player.
6.) Pray. You could still end up in a coop with only you and the other player. If you are lucky though, you are now pvping each other! You can even use normal team chat to talk to each other. Enjoy.
I think this is about all you need to know but if anyone has anything to add, clarify, ask about or fix, feel free to do so. Hopefully some time after GW2 devs will make this a little bit easier to set up.