As a mage, you only have 2 options prior to getting into the fray and getting your PvP set - stamina and stats, or damage and healing gear. Depending on the type of team you're going to get into, you will want different sets of armor (and of course spec!).
Frost mages benefit more from stats, resilience, and overall durability as a popular tactic (discussed later on) is to Ice Block early on, then do it again once or twice more, getting the enemy off of you and giving you time to maneuver more than dealing direct damage.
Fire mages can and will benefit more from damage and healing gear, such as Tailoring crafted items and heroic rewards, as they aim to burst damage fast enough so that the healer(s) aren't able to make anyone live through it in a few seconds. The bigger the crits and damage, the better a burst damage team will be in the Arena. Keep in mind that fire mages with pure +damage and crit are not as viable unless you have superior gear later on in the Arena, where everyone has lots of stamina and resilience to counter "burst" teams.
Popular Talent Builds
Popular talent builds within the Arena are, as mentioned, Fire and Ice, both with their strengths and weaknesses, a fire mage will need to make ample use of his burst abilities including Dragon's Breath, and a Frost Mage will be mainly a supporting DPS class or a slow and steady damage dealer. Keep in mind that as Arena Fights last longer, you will be needing to keep up your mana, especially if you have manashield up. Ice Block may buy you enough time to blink and bandage out, or simply give your team more staying power if you run into a long fight.
Talents aside, you will need to be using many of your PvP abilities to their fullest extent! let's take a look at some tactics.
Starting off, make sure to always create your mana gems and put up your shield(s), you will be needing all the help you can give yourself!
Depending on your team setup, you will be needing to stay in close range of your support or team mates, as a mage found solo will be killed pretty quickly.
Make sure to make full use of Polymorph and Counterspell - ideally, you will want to polymorph the healer (twice, always be ready for when they use the trinket), and counterspell a caster, if any others. If not, save your Counterspell for when the healer pops out of your sheep!
Another good target for polymorph is a warrior. Since you will only be needing to fight them when you're sure they have no support or can burst them down quickly, it's best to keep them out of battle as long as possible. In addition, polymorph will not give you diminishing returns unless you have to do it at least 4 times (usually due to dispelling), so feel free to use it as much as possible. It creates an immediate +1 advantage to your team which can be employed to win quickly!