Mage-type character's are my preferred style, and there is no one way to play as a mage... It all depends on which spells you choose to focus on...A few pointers however:
If playing as an unarmored (or low hp) mage, keep your distance! You get hit, you die, use whatever spells and shouts, to make sure your enemies don't get the chance to swing their weapon: frost spells, fear, calm, muffle, become ethereal, and slow time are some of your best weapons. If you don't have the spells, stock up on potions.
Magicka! Just like an archer needs arrows, a mage must have tons of magicka... If you run out of magicka, you die. The "novice", "apprentice", etc perks allow you to cast spells for half the cost, which means you can cast twice the amount of spells.
Back-up skills. Simply casting spells is rarely enough, a good idea is to aqcuire a few skill points in some non-magic skills, in case you face an opponent who's immune to your spells, or you run out of magic. Skills like sneak, one-handed weapons, light armor, or archery are all good choices.
Ignore "Crate"'s suggestion about "grinding" and "spamming" certain skills and spells, that is the best way to ruin the mage-experience... So yes, being a dork may be harder, but it's far more enjoyable in my experience.