Mage's Instance Tips - Before Starting The Instance
It's expected that every member of a dungeon party will cover some absolute basics before heading in:
Repair your equipment
Restock your consumables (potions, reagents, ammo)
Make lots of room in your bags for loot drops
As a Mage, there are some extra things you can do to make your teammate's run a little easier or more cost-effective:
Offer Conjured Water and Food
Buff members who benefit from an Int boost
Offering these things without being asked is also a great way to build rapport and make some friends who might be around to team up for harder content as you progress.
Mage's Instance Tips - Managing Threat While Fighting
As a Soloing or PvPing mage, quick-burst DPS with plenty of crits and high calibre pain is the route to success. "Blast 'em down before they have time to get within Melee range" is the general thought, with Frost Nova serving backup right from level 10, and the introduction of Blink at level 20.
A Mage's first goal in party battle is to target attacks upon mobs already occupied by the main or off-tank.
In an 5-person instance party, high DPS with plenty of crits and high calibre pain is also along the path towards success, but with one big difference - instances have tough, elite mobs that can destroy a cloth-wearer in a very short period of time, so DPS needs to be focussed correctly and then slowly ramped in order to allow the tanks to "establish aggro" and gain a lot of "threat" points towards themselves from the targetted mob.
If done correctly, Mages are awesome damage-dealers who have enough control that they DO NOT "steal aggro" from the tank and end up dead on the floor, providing no additional DPS to the fight.
A Mage's primary job is to support the tank while not needing services of the healer. In order to properly support a Tank, those with a DPS role, such as Mages, should be careful when targetting enemies, ensuring the mob they're attacking is being hit upon by one of the party's tanks. Targetting an enemy that a tank is not actively hitting will generally result in "peeling off aggro", with the enemy mob turning its attention towards attacking you!
If you find you're peeling off aggro in party situations even though you're targetting a mob that the main or off-tank is actively beating on, read on for a Mage's second goal in an instancing party situation, regarding keeping alive without needing the Priest to save your clothy ass.
A Mage's second goal in party battle is to temper their attacks, starting small and ramping up as the fight progresses.
Mages are extremely powerful but cannot take the beats. Thus, a Mage's second goal within a dungeon instance, aside from staying in the back of the party instead of up with the melee folk, is to temper their attacks so they still deal quality damage over the fight as a whole, but don't peel off aggro because they have done it by starting small and ramping up the DPS as the fight progresses and the tank and off-tank remain right on top of the Threat meter.
Mage's Instance Tips - Using Lower Level Spells
One key way to "start small and ramp up" involves the strategy of starting with rank 1 and 2 spells instead of the highest level available, and then moving up to the highest rank versions halfway through the fight. A bonus of this strategy is that your attacks launch more quickly because cast times are smaller on the lower-ranked spells.
You'll need to play around with your strategies a little bit while in an Instance Party in order to find the "right" sequence of spell attacks that work with the group you're currently in. Parties with tanks who are not used to grabbing and holding aggro will be more difficult to manage but can also be considered a fertile training ground for learning how to control your own toon in more challenging situations.
Jump in and blast'em out, but spend some quality time learning how to "manage threat" by targetting mobs effectively and starting small and ramping up DPS as the fight progresses.
Good Luck!