If you want to have fun with your mage, this mage PvP guide will help by starting you off in the right direction.
The PvP mage is played on two levels: Control and damage.
The good news is that they are both good in these regards, and can kill a player in no time at all.
The bad news is that their adversaries have discovered this, and therefore you will become the center of attention very quickly. So watch out for the rogue, who is your natural enemy.
A very easy build to play is a mix of Necromancer and Warlock. As your third soul, you can use Chloromancer (with zero points) or the PvP soul, Archmage. Put 34 points in Necromancer and 32 in Warlock.
The advantage of this build is that it is very resilient, hits hard and can be used in Warfronts, 1v1 PvP or questing - all with the same excellent results.
You have a pet who can deal damage; you have a debuff to remove bubbles or other buffs, together with a great deal of self-healing that can also cause damage your enemy. I would suggest this is a fairly easy build with which to start.
One of the most - if not THE most - PvP oriented soul (except Archmage, which is a PvP soul) is the Dominator. It's definitely worth having and the gain is at least a few points for PvP. You can also use it as a main soul.
If you are a control freak, you will walk the path of the Dominator. This build is very interesting, great fun to play, but also possesses a large degree of difficulty. Nevertheless, if you learn it correctly, you will indeed dominate the situation.
Dominators can silence; root; disorient; exhaust and transmogrify their enemy whilst dealing damage.
Place 31 points in Dominator and choose a damaging soul like Pyromancer to join with it. This hits extremely hard and deals a great deal of damage. Put 20 points into Pyromancer, and then take Archmage (PvP soul) and put 15 points in it. You cannot, however, do this before level 50. In the meantime, after gaining enough favor to level up, put the extra points into Pyromancer (for more damage).
With this spec, in 1v1, almost no one will be able to reach or hurt you to any degree, before turning themselves to ashes. This will mean control (eventually transmogrify - the time to heal - if you have been taken by surprise); root; move away and then burn them.
In a warfront, and against more than a single enemy, you will prefer to be amongst friends. In this case, your PvP mage will fulfill a support role instead.
Another possibility is to mix the Dominator with the Stormcaller instead of Pyromancer. The Stormcaller will especially shine in warfronts, because it is definitely the multi-targeting-master.
Nothing beats the Stormcaller when we are talking about Area of Effect (AoE). From a distance, you can protect a flag by using your AoE to interrupt the enemy when they are attempting this, whilst supporting several of your friends at the one time.
Since the Stormcaller also has great single target damage, you can use it in 1v1 as well. There is still some controversy about whether Pyromancer or Stormcaller is the better, has the greater burst etc. Don't buy into these discussions: Try them both and see which one you prefer.
Mages are ranged damage dealers. You can enhance your survivability with some souls more than with others, but you are not built to melee fight. You are built to hold your distance.
How you do this mostly depends on your style and what tactics you prefer. Whether to slow down the enemy and gain help from your pet, or to control the other and burst with Stormcaller or Pyromancer, is a question only you can answer.
Try them both and, if necessary, make changes so they are more adapted to your particular style.
There is no "best PvP mage build". It all comes down to how you prefer to play.
Use this short Mage PvP Guide as inspiration.