The first rule of mage dps is NEVER STOP CASTING. Split seconds spent hesitating on your next move will cost you more dps than simply casting the wrong spell. Always have your next spell planned before your current cast finishes. Train yourself to automatically hit the nuke key if you have no idea what to do. Just don't ever stop casting.
Now that that's out of the way, we'll move onto talents and rotations and all that good stuff.
Arcane is the current top single target spec, with Fire reigning as the undisputed king of mobility and multi-target damage. Frost can match or exceed Fire's single target damage and bring superior survivability. It's recommended to dual spec Fire/Arcane and switch as needed.
Spec advantages and weaknesses are rated in the chart below on a scale of 0-5.
Improved Flamestrike: This talent increases the damage and mana efficiency of Blast Wave by something like 200% and also greatly increases the dps of FlameStrike. While not essential, this talent is highly recommended.
Cauterize: Cheat death for mages. This is a very good survivability talent. If you have a tendency to stand in void zones or otherwise find yourself dieing often there is no excuse for skipping this.
Molten Shields: This talent allows you to activate Mage Ward with minimal dps loss. A good survivability talent for 1 point.
Pyromaniac: Solid AoE damage talent, but not as amazing as Improved Flamestrike.
Improved Fire Blast: This pairs well with Impact, making your Fire Blast easier to use from a long distance.
Use Hot Streak whenever possible, recast Living Bomb after every explosion, use Flame Orb whenever possible, and spam your filler nuke in between. Filler nuke should be Fireball, but can be Scorch while moving. Never stop casting.
In select cases where mana management is important this is not overly difficult with free, high damage Scorches. Single target rotations using Scorch do about 90% of the damage of a Fireball rotation at a fraction of the mana cost.
Current understanding of the Combustion mechanic indicate that catching a large Ignite, such as from a Fireball crit, is vitally important. Fishing for Ignite procs with Fireball and waiting for the opportune moment is more important than using Combustion immediately.
Put Living Bomb on 3 targets, use Blastwave on cooldown and spam Flamestrike, use Impact procs to spread dots when possible. Mana management is also an essential part of multi-target dps. You will not have enough mana to continually spam AoE for an extended period. Fortunately Fire specs have easy ways to dramatically improve efficiency. Use Blast Wave whenever possible as this is a very mana efficient spell. Even if you are in maximum efficiency mode Blast Wave is still good. Only using Flamestrike only when its dot is expired will greatly increase its dpm. You can further increase dpm by skipping Flamestrike and spamming Scorch with Living Bomb on a single target to fish for Impact procs. Impact procs are unreliable, but do MASSIVE AoE damage with very high efficiency.
Frost single target dps is all about proper use of procs and Deep Freeze. Deep Freeze does MASSIVE damage and should be used immediately whenever possible. Second priority is to cast as many Fingers of Frost empowered Brain Freezes as possible. Fingers of Frost nearly triples the damage of a Brain Freeze, making it worthwhile to always combo these procs together. When Brain Freeze is up, wait for a Fingers of Frost charge before using it. Always keep a spare Fingers of Frost charge handy for Brain Freeze or Deep Freeze. Only use Ice Lance when you have 2 charges. Frostbolt is the only viable filler nuke.
Performing a correct burst opener is also essential to Frost dps. Plan on using Cold Snap very early. Your burst opener should involve 2 Frostfire Orbs, 2 Deep Freezes, and 2 Icy Veins with proper use of Cold Snap.
Arcane spends most of its time in a mana efficiency mode during which the goal is to stay close to 100% mana. Arcane cycles are so efficient that this is actually possible to achieve by alternative mana positive and mana negative cycles. When attempting the mana positive cycle, Arcane Missiles and then Arcane Barrage should be used whenever possible and you need to restore mana. The mana negative cycle simply involves casting another Arcane Blast or two, increasing dps at the cost of mana efficiency. Because of Mana Adept, the primary goal while casting is always to stay near 100% mana.
Arcane also uses a burst cycle, done whenever Evocation is available and at the end of an encounter. The burst cycle involves ramping up Arcane Blast, activating all timers and then burning down to about 33% mana with Arcane Blast spam with Mana Gem used as soon as your mana deficit is large enough. Once the burst phase is over you should immediately Evocate back to 100% mana.
Intellect is now the primary all powerful stat for all mages, usually close to double the value of the next best stat. Recommended gemming strategy is to stack as much Intellect as possible while keeping your meta gem bonus. Maintaining the hit cap is still important, but less important than Intellect; the new hit cap is 1742.
To determine the new cast time of a spell after haste rating is applied, take the percentage of haste, as a decimal, and 1. Divide the cast time by that number. For example, 10% haste against on a 3 second Fireball would be 3 / 1.10, giving a new cast time of 2.72~.