Don't leave your mitt in the trunk of the car. Heat is the #1 killer of gloves.
Don't microwave your mitt or throw your mitt in the oven to break in your glove, heat will cause the leather to deteriorate and make it brittle.
Don't let your glove get wet, whenever possible. Water will promote fungal growth that will eat at the leather.
Do not heavily oil your glove; be cautious because the oil could promote rot within your glove. Heavily oiling your glove will also cause it to become heavy.
Moisturize your glove with a light conditioner. Remember that your glove is essentially made of skin; you should treat the glove like your own.
Whenever possible, after use, put a softball or baseball in the pocket of the glove to help maintain the shape of the glove. We've found that after a game using an ace bandage to help keep the ball inside the mitt works really well.
During the off-season clean the mitt with a non-abrasive cleaner. Remember the better you take care of your gloves the longer they will last.