Since the basic arena PvP goal is to kill or be killed and there are no capture objectives or NPCs to kill, makeups of teams and matchups between various classes with coordinated tactics between them are a large part of overall strategy.
2v2 Strategies[]
One strategy for 2v2, because it has fewer players than 3v3/5v5, is to Crowd Control one player consistently and kill the other off. This is often used by double-DPS teams.
One of the most common teams in seasons past is called a "drain team". This setup uses abilities such as Viper Sting, Mana Burn, and Drain Mana to deprive their opponents of mana. Once the point is reached where an opponents healer had gone out of mana It is simple to finish off both opponents. Drain teams were far more common in the arena prior to the changes to resilience that reduced the amount of mana drained by such spells.
3v3 Strategies[]
The goal is to win, you can do this by going in and blowing every single cooldown and attacking a selected target. Often referred to as 'Going Swifty.' While doing these beastly damages you should use your Crowd Control abilities such as Polymorph, blind, fear, etc. to keep the healer from healing.
5v5 Strategies[]
Basically the same as 3v3 strategy, except you make sure everyone is on one single target. This is almost a Guaranteed kill. When the first target dies the other team normally quits, so you can just /dance while they leave the arena in shame.