To clean a red brick fireplace hearth, first lay dropcloths on the floor around the fireplace. Fill a bucket with a mixture of hot water, bleach and dish soap. Dip a scrubbing brush in the mixture and scrub the hearth starting from the top and working across and then down. When you are done scrubbing, pour the mixture down the drain and fill the bucket with clean water and scrub the hearth again with the clean water. Then wipe the heart down with a wet cleaning rag. Let the hearth air dry when you are finished.