Rub a mixture of baking soda and water on the stone with a toothbrush to remove small stains.
Never put soap on a pizza stone or soak it in soapy water. Most pizza stones are made of ceramic that is porous and soap will absorb into the stone. The soap will then be released from the stone when you cook with it.
Never put a hot pizza stone on a cold surface, as it may crack.
Excessive oil buildup on a pizza stone may cause it to smoke when it is being used.