The Mage, as you would expect, is centered around using spells to get advantageous removal of enemy minions. Most of the cards unique to the Mage are either spells or secrets cards that synergize with spells and secrets, such as the Mana Wyrm or the Kirin Tor Mage.
Powerful Mage deck using basic cards: http://wp.me/p1SfP0-1Fm
All deck guides: http://wp.me/P1SfP0-1Fp
All HearthStone guides: http://wp.me/P1SfP0-1Fb
Hero Ability and Mage Cards
The hero ability of the Mage deals one damage and is best used to take out minions with low health or to help a minion take an enemy minion out or to ensure a favorable trade with another minion. When you play against a Mage avoid summoning minions with only 1 health and keep in mind that doing 1 damage is no problem for a Mage. The hero ability of the Mage also works well with the Acolyte of Pain which lets you draw a card when it takes damage.
A good basic deck uses the more powerful Mage spells, such as the Fireball and Flamstrike, in combination with solid neutral minions such as the Chillwind Yeti and Boulderfist Ogre. As an alternative you can take a lot of Spellpower minions and minions with Taunt to protect the Spellpower minions. For that deck use spells to do most of the work for you, including finishing opponents off as soon as you can.