Remove any grates or wood from the fireplace and set them aside.
Vacuum the stone fireplace with a wet/dry vacuum to remove any ashes from the walls and base.
Dampen a cloth with warm water and wring it out.
Wipe the stone fireplace with the cloth to remove soot and ash not cleaned away with the vacuum.
Fill a bucket with 1 gallon of warm water and add 3 tsp. of dish detergent or natural stone cleaner according the to the manufacturer's instructions. Fill another bucket with clean water.
Dip a soft-bristled scrub brush into the soapy water and scrub the flagstone fireplace to remove all traces of soot. Clean one area at a time and rinse with a cloth dipped in the bucket of clean water.
Wipe the stone fireplace with a towel to remove any excess water.