As an arena player, you must keep in mind that your gear will need to vary significantly from the PvE gear you're used to having. For all specs, you will need Resilience gear, and resilience / stamina gems in them. Ideally, you should go PvPing to the battlegrounds as well and obtain all the Veteran armor you can, as it all has +resilience and +stamina.
Why do you need stamina and resilience and not spellpower and the others? Simple, high crits will kill you quickly, and you want to avoid that as much as possible. Once you have enough arena points to spend, you should first spend them on gloves for the only extra effect you get - 50% chance to resist interruption on fear! then go for the 2 piece bonus.
Don't forget, first and foremost, to use (or buy!) your Insignia to remove all effects impairing your character from being controlled from the Honor vendor!
Popular Talent Builds
All 3 Talent Builds are worthwhile provided you go for each's ultimate and mix & match the remainders. It depends on your playstyle and your teammate(s) to be the best you can be in the Arena. Outlined below will be the use of each:
Affliction: The author's favorite. Effective in all arena matchups, this build lets you cast unstable affliction on your enemies, stopping the paladins from mass-cleansing your DoTs or forcing the paladins/priests to heal themselves or bubble instead of cleansing themselves! Should they do it anyway, it's a surefire damage spike that can lead to your victory. Don't forget to use instant Howl of Terror!
Destruction: High and fast numbers, protection vs shadowpriests and warlocks - this build allows you to use a high damage output at the expense of no DoTs and less mana than the others. Ideal in 2v2 and 3v3, starts to lack some in 5v5s that are not burst teams. If paired with another high damage class like mage or another warlock with the same spec you may see numbers rising quickly, goal being to kill your enemies before your mana runs out and before they can heal.
Demonology: Stability - you will be nearly unkillable if they focus you since you use soul link and have improved resilience and HP thanks to the demonology tree's talents, your goal should be to DoT your target and cast fears around to disrupt enemy tactics while having your pet on the healer / manauser.