Take a dry rag and wipe off as much of the residue as possible. Use a rubber spatula to remove any stubborn spills, being careful not to damage the surface of the stone.
You can also bake off any heavy spills. Instead of turning the oven off when you are through baking, turn it up to the highest temperature setting for 60 to 120 minutes. This will charcoalize the residue on the stone.
Remember, baking stones naturally darken and discolor with continued use. The grease and toppings that drop on the stone actually improve the baking properties by sealing the surface of the stone and minimizing the chance of dough sticking to the surface.