Mahogany has an open grain structure. As a result, the wood will stain unevenly if you do not use a grain filler on the surface. This is the main difference between refinishing mahogany and other woods. Any stains applied over the surface of mahogany should compliment the natural reddish tint of the wood's surface. Refinishing mahogany is not a difficult process, and can be completed in just one weekend.
Spread a dust sheet under the mahogany piece where you will refinish the wood. Outdoors or a well-ventilated garage are ideal locations.
Apply the solvent stripper to the surface of the wood with a soft cloth. Allow it to sit for 10 minutes. Use a putty knife to scrape away the seal on the surface of the wood. Use steel wool to scrape away any sealer from the corners and other hard-to-reach places.
Rinse the stripping solution with water and dry with soft cloths.
Sand the mahogany lightly with 120, then 220-grit sandpaper. Wipe the sawdust away with a soft, damp cloth. Allow the wood to dry for 10 minutes.
Apply the grain filler over the mahogany with a soft cloth. Work it into the grain of the wood. Allow the filler to dry for 1 hour. Scrape away any filler that remains on the surface of the wood with a putty knife. Sand lightly with 220-grit sandpaper.
Pour some stain over a soft cloth and rub it into the surface of the mahogany along the grain. Allow the stain to sit for longer if you want a darker stain. Work in small sections, overlapping slightly with any sections bordering the section you are currently working on. Wipe any excess stain off with a clean rag. Allow it to dry for 2 to 3 hours.
Brush a coat of polyurethane sealer over the wood with a paintbrush. Brush along the grain. Allow it to dry for 2 hours. Sand lightly with the 400-grit sandpaper and apply another sealer coat. Allow the mahogany to completely cure and dry for 24 hours before using the furniture.
Always wear a dust mask when sanding, and always wear safety goggles when working with sandpaper or chemicals.