Scrape the surface of the mahogany with a plastic putty knife to remove any excess grain filler after you have allowed it to dry for about 1 hour. Once the surface is relatively flush, sand the mahogany with 220-grit sandpaper until the surface is smooth.
Apply the stain to the mahogany furniture with a brush, roller, sprayer or rag -- always apply with the grain. Allow the stain to sit for about 5 minutes, then wipe away the excess with a clean, dry cloth.
Apply additional coats of stain as desired. Let the wood dry completely between each coat of stain.
Apply a protective topcoat to seal the mahogany and grain filler. Shellac, varnish, lacquer and polyurethane are all common options for this process. Most can be painted on with a foam applicator brush. However, if you use polyurethane, you need to sand with 400-grit sandpaper after the first coat dries, then apply a second coat.