Although the main character in "Planescape: Torment," The Nameless One, starts out as a sword-swinging fighter, you can train him as a mage if you're in the mood for something more cerebral. If you're looking to channel your inner arcane energies, Mebbeth the midwife can help you become a mage.
To excel in being a mage, you'll want to make sure you have a high Intelligence (INT) score. If you want the mage specialization bonuses, you should switch from fighter to mage before level 7. It's best to stay as a fighter until at least level 4 or 5 in order to build up your hit points and other combat stats.
You can find Mebbeth in the Midwife's Hut in Ragpicker's Square, located just below the center of the area. Ask her if she is a witch; she will begin a conversation in which she offers to teach you magic. After a few fetch quests revolving primarily in and around the Market, she'll train you as a mage and give you some useful items, such as the Scroll of Chromatic Orb.
If you get tired of slinging spells, there are NPCs who can retrain you as a fighter or let you try a new class: the thief. The thief trainer, Carver, is also located in Ragpicker's Square, while the fighter trainer, Porphiron, is east of the Flophouse. Alternatively, your party NPCs can help: Talk to Dak'kon if you want to be a mage or a fighter, while Annah can help you become a Thief.