1) Water daily -- This should be a no-brainer, but make sure to check the tree's water supply daily and always replenish it when it starts getting low. (They're thirsty little suckers.)
2) Extinguish any candles that may be lit on or around the tree.
3) Make sure all lights bear the UL mark of safety before stringing them around your tree.
4) Always unplug lights when you are sleeping or away from home. (Or put them on a timer so they don't stay on 24 hours a day.)
5) Saw off the base of the tree before putting it in the stand so it will better absorb water.
6) Add an aspirin tablet or a few pinches of sugar to the water -- it's an old wives' tale, but some say this helps the tree last longer.
7) Always keep trees away from baseboards and heaters; otherwise they'll dry up.