Summarize this article:

Mix two to three tablespoons (15 to 45 ml) of a mild soap or detergent into the water. Mix the water and soap together until they are well-combined.  Alternatively, you can purchase a specially formulated limestone cleaner from your local hardware store to clean your limestone fireplace. Do not use soap that contains ammonia, vinegar, bleach, acids and other harsh chemicals commonly found in household cleaners to clean your limestone. Squeeze out any excess water. Starting from the top, begin to wipe down your fireplace. Cover the whole surface with the solution. Then let the solution set for one to two minutes. Alternatively, you can use a soft sponge, like the sponges used to wash cars, to clean the limestone. After the solution has finished setting, dip your cloth in the solution and wipe down your fireplace again. Use more pressure this time to remove visible dirt and debris. You may use a very soft bristle brush or toothbrush to remove stubborn dirt, as well as dirt from small crevices. Pour the soap solution out and refill the bucket with clean water. Dip a clean microfiber cloth into the water, and squeeze out any excess water. Then wipe your fireplace from the top down until all the soap, dirt, and debris are removed. Make sure to rewet your cloth in between wipes for a thorough clean. Or use a dry, microfiber cloth to dry your fireplace. Wipe your fireplace down with the clean cloth until it is completely dry.

Summary:
Fill a bucket with warm water. Dip a microfiber cloth into the water. Wipe down your fireplace. Rinse with water. Let the limestone air dry.