The secret to getting the most out of leveling with someone else is in understanding exactly what your class brings to the duo. For a pure dps class, one with no pet and the survivability of a cloth-wearing snowball in hell, the mage can be a powerful addition to a pair.
First, the obvious utility spells. Conjured food and water mean you can avoid spending gold on these. Time between fights is reduced when you can recharge your mana-batteries quickly and easily. The portals you won’t get until 40, at which point you can get from Kalimdor to the Eastern Kingdoms a lot faster than a group with no mage, making Fedex quests a breeze. Dampen and Amplify Magic are almost totally useless spells – unless you’re leveling with a warrior and receiving no healing anyway, in which case reducing the magical damage you might take is great. And Feather Fall is situationally useful.
Second, crowd control. These days nobody uses it at high levels but you can and should use it as you level up. Convince your partner to let you sheep things at the start of a pull. Frost nova and blink away from mobs. Use frost bolts to slow things down. You’re more likely to survive when one of the six gnolls that want your spleen is suddenly a fluffy sheep and the rest are struggling across frozen ground while pelted with shards of ice.
Third, sheer firepower. It’s hard to match a mage for damage as you’re leveling up, and if you’re leveling with someone specced into healing especially you’re going to be doing the lion’s share of the killing. Just remember that especially in the first fifteen levels you are going to pull aggro off your partner even if you’re teamed up with a tank class, and be ready for it.
Tips for Leveling
First, do not spec Arcane. Arcane is not viable until you get Arcane Blast at level 64. Your choices are to level Fire or Frost. A mage who is planning to do a lot of soloing should level Frost. This is also a good spec if you are leveling with a healer or with some other squishy dps class. You can slow things down and kite them while taking little damage yourself.
However, if you’re leveling with a tanky class, you might spec Fire instead. Let your meat shield pick up aggro while you lob balls of fire at the kobolds’ heads. There are plenty of sites out there with leveling mage builds and I won’t replicate that here, but here’s a fire and here’s a frost that are pretty cookie cutter.
You and Your Partner
If you are paired with a warrior, hunter, enhancement shaman, ret paladin (at early levels, or prot later) or feral druid: Spec fire, let your partner or partner’s pet keep aggro on the mobs. Kill things. Don’t pull aggro; cast fireballs and pyroblasts at one mob as a time as long as the tank isn’t dying. This can work with a warlock with a voidwalker out too but warlocks and mages are bad pairs. One second you’re questing, the next second you’ve destroyed two or three countries and your hair is missing.
If you are paired with a priest, balance/resto druid, some sort of shaman that isn’t enhancement (I don’t think they’re doing it right. Unless she’s a resto shaman and you’re doing a lot of LFD), holy pally, or rogue: Spec frost. Plan your pulls carefully. Sheep things, then use frost nova to trap them, empowered blizzard to slow them. Kite ‘em, shoot frostbolts, don’t let them near your partner if he’s healing you.
Either way, things are now dead. Sit down and have some conjured bread and water. Steal the kobold’s candle. Profit.
Other things to consider: Try to get your partner to role a class that does not wear cloth. If you’re teamed with a warlock or shadow priest, you’ll be fighting over gear. You aren’t likely to find a wand until level 15 or so, unless you get lucky, so you might have an enchanter make you a low level wand (the mats are pretty darn cheap). You’ll want a wand; at low levels your mana can disappear fast and leave you no way to kill the mostly-burned-to-death boar that suddenly isn’t dying. Do a little research as you level up to learn real details; this is supposed to give you a feel for the flavor and fun that a mage brings to a pair.