The WOW Mage is simular to Mage's that you might have seen in other fantasy games. In a nut shell the Mage is magic oriented and not much into melee fighting. The world of warcraft Mage fits this description, but the magical abilities of the mage of world of warcraft makes it a formidable character.
The Mage character class should stay clear of any hand to hand fighting, it is designed purely for fighting from a distance. The Mage can deal out incredible damage but without any self healing capabilities the Mage does not bode well under fire. Some great benefits that a Mage provides for their party are conjuring of food and water, they have awesome offensive spell casting skills and a really cool ability to teleport themselves and their party to world of warcraft capital cities.
Racial traits you should review for your WOW Mage:
The fact that the Mage class has no way to heal itself makes the draenei race a good race to consider for its Gift of the Naaru healing ability.
Along the same lines as the draenei, the troll race is helpful with its regeneration ability, though not quite as effective as the Gift of the Naaru.
The blood elf is a popular race for the Mage with its Arcane Torrent and Arcane Affinity. Some say the blood elf makes for the best Mage but thats a matter of opinion.
The gnome makes a good Mage with its Expansive Mind to replenish mana and Escape Artist is very useful in getting out of sticky situations.
The diplomacy of the human race is good for reputations in the future and Human Spirit helps to reduce downtime, although their Sword and Mace specialization is not of much use to a wand carrying Mage.
The forsaken race only helps the Mage when battling a priest or warlock and little else so I don't recomend them unless you really want a challenge.
At the very start, no matter what character class or race you are playing I recommend keeping it simple. Learn the basics of your character and get a good understanding of your characters skill's and abilities. Do your best to only stay in combat for short periods of time.
Use range weapons and spells to keep your character out of harms way. But don't misinterpret this as just fooling around. Use this time to concentrate on completing quests and plenty of them. If you think you have completed all the quests in your present area check again to be sure.
Each Mage trainer will have new and valuable information for the world of warcraft Mage, so learn all you can. Besides trainers, each area of world of warcraft will provide new spells and information that you will want to get for your Mage. The Mages choice of professions should not be taken lightly, the mage can only wear cloth so tailoring and jewelcrafting are of use to the Mage. A mount will come in very handy to the world of warcraft Mage, so think about getting one as soon as you hit level twenty.
Some people may disagree but I find the Mage to be one of the easier classes to play at the beginning levels. Early on the Mage will rely on it's powerful Fireball spell to defeat it's foes from afar. Also the Mage starts off with Frost Armor which is a great self buff making leveling easier. When the Mage uses these two spells together it will make leveling go much faster.