I just hit level 70 on my WoW Paladin alt and I want to be able to PvP with it. What is a good PvP build for my Paladin?

This is a difficult question to answer because PvP is a very general category. The best build is going to depend on what situation you are encountering PvP. If you play on a PvP server and are concerned about surviving ganking attempts while out in the world, the best build is going to be part protection part retribution. If you are in an arena the best build is going to be a mix of holy and protection. If you are in a battleground, well, everyone is going to WANT you to heal but you may be able to do a little damage with a protection/retribution mix. Lets break it down a little bit further.

Arena Specs
The generally accepted “best spec” for arena Paladins is 41 holy, 20 protection. Key talents included in this build are 2/2 Stoicism, 5/5 Spiritual Focus, 5/5 Illumination, 3/3 healing light, Blessing of Kings, 3/3 Impoved Righteous Fury, as many points into Toughness as possible, and 3/3 Improved Concentration Aura.

Soloing Specs
If you are a paladin and want to be able to kill most people in a 1v1 situation, your best bet is to go with a protection/retribution mix. This will also be the preferred spec for soloing in most PvE situations as well, so it works out.

Battlegrounds
Usually the key to whether a team wins in a battleground or not is dependant on their healing. Because of this most people are going to want you to heal in battlegrounds. If that really isn't your style, go for a heavy damage and survivability build, much like a soloing spec.