The best way to clean natural stone tile grout is with a diluted bleach solution. First, mix 1 part bleach with 9 parts water. Wet a rag or sponge in the solution and scrub the grout until it's clean. Be sure to rinse the area well after cleaning to remove all of the bleach residue.

The first step is to remove any surface dirt or debris with a stiff brush or vacuum cleaner. Next, mix together 1 part baking soda and 2 parts water to form a paste. Apply the paste to the grout and let it sit for 10-15 minutes. Finally, scrub the grout with a stiff brush or old toothbrush and rinse with warm water.