Mop the marble floor with a damp mop to remove dirt and dust so you can effectively clean the water marks without rubbing dirt into the stone.
Rub 0000 steel wool gently onto the surface of the water mark or ring. The finest grade of steel wool will buff out the water marks without badly scratching the marble.
Polish the marble floors. Purchase a commercial marble polishing powder or spray, and follow the directions carefully. Generally, the solution needs to be buffed onto the marble with a soft washcloth to fill in the scratches and polish the marble.