Paladins are a hybrid class, but this doesn't mean 2 of their 3 builds are effective in the arena. If you want to be effective and be the best you can be for your team, you will need to put that heavy defense / block armor away, stash your high DPS two-hander, and go with a healing 1-handed weapon + healing shield. Unlike most other classes, you will not be needing a lot of resilience since you will be wearing plate and you are able to bubble, heal and get yourself out of trouble, usually paladins are the last to die in most arena matches (you WILL be getting crowd controlled, enough to break your cooldowns and trinkets), since you have the best survivability of them all.
Paladin DPS is sub-par compared to the boon you give to the team with your heals, Blessings of Protection, sacrifice, auras, and more importantly dispels, so you need to focus your gear and your spec toward the holy tree, ideally.
As with all classes, the best PvP gear will be found within the battleground honor points (for veteran armor and current season resilience, stam and healing epics), and arena points (for your set gear!)
Popular Talent Builds
As mentioned, the one and only popular paladin role in the arena is support, cleanser and healer. Paladin DPS is unreliable and while it can score high crits sometimes it just doesn't allow for the opportunities to attack without your teammate suffering or benefitting more from your support. A holy based spec so you can heal best and keep yourself alive is recommended.
Always stay within Line of Sight of your teammate(s), and be wary for Unstable Affliction. Should you detonate an unstable affliction you will be in for a quick loss if the other team is experienced, since it silences and damages you.
Keep an eye out on the enemy your teammate is attacking, if he tries to run away due to low health, always use your hammer of justice to stun them enough to finish them off. Another useful tactic is to stun rogues who cloak of shadows or healers about to throw a big heal out there. Being able to multitask between cleansing, healing, and stunning is the mark of a good player.
If the other team focuses you first, they want you to blow your bubble as quickly as possible. Try to delay it as much as you can, as they will then focus on your teammates then return to finish you off. If this happens, be ready with a blessing of protection on your teammate(s) so you disrupt their strategy.
Avoid using your bubble on fears or sheeps unless absolutely necessary, as mentioned above, the main point a team will try to make when seeing a paladin is trying to make them waste their bubble so they can have the upper hand. Use your PvP trinket!