Attention! When deciding which type of mage to play (focused on fire, frost or arcane magic), keep in mind that frostmages deal much higher damage with the new rank 11 of Frostbolt. The skill is taught by Tome of Frostbolt XI which you can find in Ahn'Quiraj (20 players). You may try to get the book in the auction house but be warned: there are a lot of other mages looking for it. Also prepare to pay a huge amount of gold for it. Prices vary depending on your server but the average price is about 1100 gold. Or join an AQ20 group if you want to and see if you find one. I will leave it up to you to decide whether rank 10 of frostbolt is worth playing a frostmage or not. See difference in damage here.
Most Frost spells will cause a chilled debuff on the affected target. With frostbite this can be improved to be a frozen debuff. Frost mage typically fall into two categories:
Winter's chill, frostbite, improved blizzard, permafrost, artic reach
Utilize the extra chill time to get distance and start AoE again (thus repeating the cycle). This is extremely powerful in soloing (farming) large groups of melee npcs. Also useful in Alterac Valley.
Piercing Ice, Ice Shards
Utilize the 100% crit damage to output high dps. Frost mage going for this build needs to collect many +spell damage or +frost spell damage items in order to make this work. In addition, with the trinkets and short frostbolt cast, followed by instant Cone of Cold, this can be formidable in pvp situations as well.
There are some debates regarding the benefits of the Ice Barrier (frost talent 31), since it is easily overriden by PW:S or purged by shamans. As such, it probably is mostly a PvE skill. Some frost mages are (30/21) frost/arcane builds.
Commonly aimed for PvP, the fastest way to convert your mana into as much damage as possible.
Unfortunately, people geared for Molten Core usually have a high fire resistance, just as the mobs there too, so Frostmage is currently favored by many. Although since recent patches where Curse of Elements have been improved for both Frostmage and Firemages, fire mages are quite capable of damage output in Molten Core.
Common Instance spec'ed build. On average, an Arcane-geared mage possess less pure damage capabilities than a firemage, yet they have a multitude of other useful abilities. They can be used as crowd control with the Polymorph spell, dish out burst damage when other spells are coupled with the Presence of Mind talent, and increase/decrease damage input and output with the Amplify and Dampen magic spells. Many mages choose to invest their time in a dual-build nature, involving either Fire/Arcane or Frost/Arcane.
What talents you choose depends on your playing style, but there are a few popular builds that most mages go for. The 33Fire/18Arc, 33Frost/18Arc, 30Fire/21Arc and the 31Arc/20Fire Variations of these can be made by individual mages to suit their preferances.
This is a standard fire build going all the way down to the Tier 7 talent including Impact for some limite kiting help.
A popular Frost build. It's used to freeze targets with Frost Nova and then attack them via critical hits from Frostbolt or Cone of Cold. Ice Shards, Shatter and Frostbite combine together to form a lot of critical strikes power. Improved Blizzard and it's effect should allow mages a chance to pull off more AoE's while their opponent is slowed. With a talent point in Arctic Reach, you have more of a chance to stop sapping Rogues and intercepting Warriors. With only 3 talent points in Frostbite, you may not proc as often, but at least you're not proccing when there's nothing else around. It's sort of the same issue as Clearcasting; a free spell and no one to use it on.
Also, with a slowing/freezing build like this, your fire damage can be used a lot more often. With the enemy at bay you worry less about your casting time. Also, instead of hoping you slow down your enemy, you can also rely on the fact that even if they aren't stopped your critical hits are doing pretty nice damage. Consider this build as a way to get close to fire spell damage while kiting the enemy at the same time.
A Fire build that also allows for Presence of Mind from the Arcane tree. This talent can be used in combination with Pyroblast or Flamestrike for some good instant cast damage. And instant castPolymorph or Frostbolt can also be useful in many situations. Many fire mages prefer Presence of Mind over Combustion.
5 Improved Arcane Missiles
5 Arcane Concentration
5 Improved Arcane Explosion
2 Improved Counterspell
2 Improved Mana Shield
1 Presence of Mind
4 Arcane Mind
3 Arcane Instability
1 Arcane Power
Here is a link to the talent calculator for a mage on the wow-europe website.
Note this is for a mage on the current version of WoW, as the new patch comes out the talent board will change with new patch. The calculator is found at this link. (This new table is only a small change but is very good for PVP fire mages).