Sweep your limestone steps to remove dirt and sand, getting them as debris-free as possible. To simplify cleaning, wipe up spills when they happen, before they soak into the stone. If they soak in, they may stain the limestone.
To protect your limestone steps, avoid cleansers with vinegar, lemon or other acids. Stay away from abrasive cleaners that may erode stone. The World Floor Covering Association recommends castile soap or a similar mild soap for cleaning limestone.
Once you have swept the stairs, prepare a bucket of 1 gallon warm water and 1 tbsp. castile soap. Mop the limestone steps with this mixture to clean them, then go back over the steps with a dry mop to sop up extra liquid and prevent streaks as the stairs dry.