Sweep out the fireplace with a small, handheld broom. Sweep up the ashes and throw them away.
Line the floor of the fireplace with old newspapers. This will catch the ashes or soot that falls when you remove the damper.
Remove the chimney damper plate. The process will vary depending on how your damper is installed. Most dampers connect to their supports with screws or cotter pins. Slowly pull the damper out of the chimney. Dump any ashes on the plate in the trash.
Hold the damper over the newspapers and scrape it with a wire brush to remove the large chunks of soot.
Fill a gallon bucket with 6 tbsp. of TSP cleaner, 1 cup of bleach and 1 gallon of warm water. Dip the scrub brush in the mixture and gently scrub the front and back of the damper to remove all the soot. Rinse the damper with clean water. Dry it with a clean towel and replace it back in the chimney.
Remove the newspapers and throw them away, then vacuum the fireplace with a shop vacuum to remove any remaining soot or ashes.