The first important step in caring for your natural stone tiles is to seal them soon after you install them. A good sealant will last for a few years, but should be periodically reapplied to remain effective. The sealant will help protect the tile from water damage or oils.
When cleaning your floors, steer away from acidic or harsh cleaners, as these can damage the stone. Instead, use a stone or tile cleaning product with a neutral pH. That will be a 7 on the pH scale. Acidic products will most likely dull the surface of your stone tiles and eat into them. Also, make sure not to use harsh scouring pads or similar products that could scratch your floor.