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Dana,

Keep your stone surfaces dry by dustmopping often or using a neutral spray cleaner with a microfiber mop. Natural stone does not need to be treated on a daily or weekly basis with water.

Water will push dirt and dust into the lowest parts of the stone and grout causing build-up that looks like dirt. This fools home owners into mopping more. I operate a Natural Stone Restoration company that performed work on more than 2 million square feet of residential stone last year. Most of that was deep cleaning or refinishing limestone and travertine that had been improperly over-mopped.

Dust mop often. Vacuum often. Spot clean with neutral cleaner where necessary. Have your floor professionally restored or maintained only when you see the maintenance getting away from you.