It is important to clean natural stone  regularly especially polished ones to remove abrasive substances.Cleaning with a neutral pH-7 stone cleaner can be done to clean all finishes, ie:polished, honed, textured.One product highly recommended for daily use is Lustro Italiano stone cleaner.Whatever product brand used  be sure to follow manufacturers recommendations.

For honed and textured surfaces a "stone soap" can be used. Stone soaps are a combination cleaner and conditioner product generally formulated from natural vegetable oils. They leave behind a residue that acts as a soil releasing agent on textured surfaces,they can also provide added stain protect and on some stones develop an attractive patina. 

Periodically a thorough cleaning is advised. A maintenance program will help protect your natural stone surface.