The Sorceress has Cold Spells, Lightning Spells, and Fire Spells. None of this silly offensive and defensive stuff for her! What ever happened to Earth and Wind? Ah well, on with the class.
First, the bad news. The Sorceress doesn't have any spell or skill or anything to allow her to heal. Perhaps the assumption is that she'll stay far enough away from the action that nothing will ever touch her. It's therefore extremely important for a Sorceress to find helmets, weapons, and so on that assist with healing. Also, always carry a number of healing potions.
When you being as a young Sorceress, you have a staff that grants you Level 1 of Firebolt. It's good to build up on at least two of the styles of magic, since you occasionally hit monsters that are immune to one particular style. It seems you hit a lot of fire resistant creatures early on, but there are also plenty of monsters resistant to the other two.
Since magic is a Sorceress' primary weapon, you can use this off the left mouse button.
Warmth on the Fire side is a passive skill - this increases the rate at which you recover mana. This of course is rather good for a magic-user to know quite a bit :)
Lightning Bolt, which you have to wait for level 12 for, does 1-40 damage which is pretty impressive. Fireball does 6-14 to every creature within 2 yards, so that's good for mass combat situations.
There doesn't seem to be any innate advantage of one style vs another - it's merely a matter of which monsters you are currently facing, and what they are immune or sensitive to.
Diablo 2 Walkthrough
Walkthrough Master Index