Equipment
Rent a floor buffer or sander that is capable of using diamond sanding pads. When you visit the rental store, ask the staff there which machine they recommend to use with diamond sanding pads and stone flooring. You will need a machine that offers RPMs between 157 to 350. You will also need to purchase some diamond sanding pads with varying grits. If the machine that you rent does not offer a holder for diamond sanding pads, purchase or rent a drive plate that attaches to the buffer and will hold a diamond spacer.
Preparation
Eliminate all coatings from the floor. This can be done with a chemical stripper or by hand. A combination of both methods will probably be best for older floors that have been used as a main floor or as a subfloor. Cover the baseboards with plastic or tape. Lay plastic sheeting over surrounding carpet and anything else that could be damaged by water. Remove all furniture from the room. Attach the diamond sanding pads to the buffing machine. If there is a water tank included with the buffer, fill it with water. If not, use a mop to dampen the floor.
Sanding
Start sanding with the coarsest grit pad. Grind the floor 6 to 8 inches away from the walls all the way to the center of the room. Walk in a straight line and grind the entire floor two to four times. Vacuum the area with a wet-dry vacuum to collect dust. Wet the floor again and sand with the next highest grade paper. With each change in sanding grade, get a little closer to the walls. The finest grit sander can be used flush with the wall. The is done to prevent grinding of the baseboards and to keep water from collecting on the sides of the room.
Cautions
Always follow the safety instructions for the buffer machine. Make sure the machine is safe to use in water before starting this project. Read all manuals that come with the sanding machine. Always wear eye protection and a respirator to prevent dust from getting into your lungs. Do not let children near when operating the machine.