Frost Mage - the PvP spec. Specializes in locking everything down for their allies to kill. Uses Frost Armor to slow attackers, Water Elemental to Freeze from afar, and Frost Nova to freeze nearby enemies. As a PvE spec, very good for soloing quests. Either you or the Water Elemental mob everything up, freeze it in place, then drop Blizzard on it. In groups, it's not as good, because using Blizzard on everything in an instance is the fastest way to pull aggro off the tank and piss your healer off when everything comes to chew on you. That only leaves you with Frostbolt and Ice Lance to use for your primary damage sources, and you could do much better with Arcane or Fire.
Fire Mage - the PvE/PvP spec. In PvP, you should be using Scorch almost exclusively, since it costs you no mana and you can move while casting it. You want to try for as much crit as you can so you can get Hot Streak procs left and right. Never stop moving as a Fire Mage. It'll be up to you if you want to use Mage Armor for the debuff reduction and mana regen bonus or Molten Armor for the crit boost. In PvE, you'll open with Pyroblast on boss fights and follow up immediately with Living Bomb once you talent for it. Otherwise, all you need to do is make sure the Critical Mass debuff stays on the boss and you shoot as many Fireballs as you can at it, throwing Hot Streak procs when you get them - but holding them for a moment or two if you literally just shot one off. It's better to let the Damage over Time tick than it is to shoot off two Pyroblasts in a row. Yes, two Pyroblasts is lots of lovely damage, but the Hot Streak proc will stay on you for a good 15 seconds. That's plenty of time to keep shooting Fireballs and wait for a few more ticks on the boss from your original Pyroblast. Once you get Living Bomb, you should open the boss fight with Pyroblast, Living Bomb, then Combustion. If you run out of mana during a boss fight, which is likely as a Fire Mage, just spam Scorch until you get more Hot Streak procs. It's free DPS, even if its reduced.
During non-boss encounters, you want to open with Scorch so you apply the Critical Mass debuff, then follow up with Living Bomb. Pyroblast is too slow to cast during mob-pulls, so you should only use it when you have Hot Streak. If you GET Hot Streak early in the fight, target a high-health enemy, cast it on him, hit him with Living Bomb and then Combustion. Throw a Flamestrike or a Blast Wave under the entire mob and hope for an Impact proc - then hit the Combusted target with Fireblast, and spread all the DoTs through the entire mob. Your DPS will jump once everything has DoT ticks going off, and the mob will typically fall apart almost instantly. This is really the only time you should be using Combustion against anything that isn't a boss, during a dungeon.
Arcane Mage - the single-target PvE spec. The only way you'll ever want to play Arcane Spec in PvP is if you're a top-tier genius Mage player who has some amazing partners to work with. Otherwise, this is THE spec for boss fights, as it has the highest single target damage output in pretty much the entire game - usually. As balance between classes is tweaked, Mages will go up and down on the list, but they usually stay in the top three.
The Arcane Mage is usually mocked for the incredibly simple rotation is has, oftentimes jokingly called the One-Button Rotation class. It's very straightforward - open a fight with Arcane Blast until you get 4 stacks of the Arcane Blast 'debuff', then throw Arcane Missiles. If you go five or six Arcane Blasts without generating an Arcane Missiles proc, throw your Arcane Barrage to clear the debuff - if you keep casting Arcane Blast with 4 stacks up, you're going to run out of mana in about ten seconds. Open boss fights with Arcane Power on the third Arcane Blast cast. You don't want to waste time building stacks of Arcane Blast with that amazing damage buff.
Don't forget to take the Focus Magic talent - even though you can't cast it on yourself, putting it on the healer or another cast-spamming class (especially Elemental Shaman) is a good way to get yourself an occasional 3% crit rate buff. Sounds low but it really does add up, especially if you glyph for Arcane Missile crit rating. Presence of Mind is another good talent to grab. You'll want to make a macro with it and use it in emergencies, both in groups and out.
This is the macro, letter for letter - very straightforward.
/cast Presence of Mind
/cast Polymorph
Since Presence of Mind, or PoM, isn't on the Global Cooldown, using it means it won't trigger GCD and you can immediately follow up with another spell. In this case, you want Polymorph in case you pull something you didn't mean to, or someone breaks the CC in an instance run. This macro is typically called PoM-Poly, and tanks love it when you know how to use it properly. There are other places to use PoM, but as an Arcane Mage, that's pretty much gonna be it. If you need an emergency slow, you COULD use Frostbolt instead of Polymorph, but Arcane Mages have an insta-cast Slow spell anyways.
Until you get to Cataclysm instances, there will never be a reason for you to spam AoEs in a dungeon. If you're Frost spec, Blizzard should only be used when you're alone. In a dungeon, you should be swapping to your alternate spec. As Fire, only use Blast Wave to cast Flamestrike - there's a talent that makes it auto-cast Flame Strike on the same location if Blast Wave hits two or more targets. Even though a Fire Mage gets insta-cast Flamestrikes, it's still not a good idea to spam that for AoE damage as it'll murder your mana. Use Pyroblast+Living Bomb+Combustion+Impact to deal your AoE damage. As Arcane, even though there's a talent to reduce the cost and global cooldown of Arcane Explosion, letting you shoot off nearly two per second, you don't want to do that in a group. It's the FASTEST way to pull aggro off your tank, get yourself killed, and likely cause the mob to go after the healer, who started panic-healing on you as fast as they could, thus shoving their aggro through the roof, and now the healer is being mauled.
A good Mage can carry a group through an instance. A bad Mage can wipe it, repeatedly.
