Leveling an arcane mage is a simple process. Most of the talents you want are in the Arcane tree and any branching out will happen at later levels to flesh out the spec. Some players will choose to go with a spec that is a little more survivable, while others will simply level in a raiding spec to get used to the rotations. The best part about playing an arcane mage is you have plenty of options.
Staple talents for the Arcane Mage are:
Arcane Stability 5/5 - Arcane Missiles can not be interrupted
Arcane Concentration 5/5 - Clearcasting for free spells
Presence of Mind 1/1 - Next spell is instant cast
Arcane Potency 2/2 - Increased Crit rate while clearcasting
Arcane Instability 3/3 - Spell Damage and Crit rate increase
Arcane Flows 2/2 - Lowers the cooldown on some major spells
Missile Barrage 5/5 - Speeds up your Arcane Missile Casting
These are baseline talents that every arcane mage will typically have. With these to work around you can decide on many other options.
Some players like to go into the Fire tree for Pyroblast. With this you will lead with the Pyroblast, as it has a long casting time (and does major damage). After Pyroblast, you can cast a Frostbolt to slow your target, or simply start casting arcane missiles. If things get rough you can activate Presence of Mind and cast an instant cast Pyroblast on your target to bring it down quickly.
The one talent in the fire tree that most arcane mages will want to have is Incineration, for the Arcane Blast damage increase. Do not get this talent early, as you will not get that spell until you are higher level.
Frost talents you should consider are Precision (hit rate increase) and Icy Veins (spell haste buff).
