There are many species of mahogany, some softer than and some twice as hard as red oak. Whether soft or hard, mahogany needs extra protection when you use it on high-traffic areas like stairs, where it is likely to be dinged and scuffed. Luckily, it shows well with a dark stain that hides imperfections, and you can add an extra coat or two of finish without masking the grain. A high-quality polyurethane floor finish works well on all species, but softer ones, such as African mahogany, may benefit from the extra protection of spar varnish.
Mask off the top and bottom edges of the risers, where they meet the treads, with 1-1/4-inch masking tape.
Sand the treads with an orbital sander and 120-grit sandpaper. This will knock down the grain and open it so it will accept stain more evenly. When you are finished, change the grit to 150-grit and sand the treads again to remove scratch marks from the previous sanding. Finally, go over the treads once more by hand with the 150-grit paper, sanding with the grain.
Wipe the treads with a damp cloth to remove sanding dust.
Brush stain onto the treads with a paintbrush and wipe it off with a rag before it has a chance to dry. It is best to do this in stages, brushing on a little, then wiping with the grain, to get the most uniform colour. Let the stain dry for two to four hours before applying a finish.
Apply polyurethane or spar varnish to the treads with a paintbrush, painting with the grain of the wood. Start at the back of each tread and work toward the front, finishing under the front edge. This is easier to do if you start at the top of the staircase and work down.
Let the first coat of finish dry at least overnight--some brands of spar varnish may take even longer. When it is dry, scuff up the surface with 220-grit wet/dry sandpaper to knock down the grain. It is not important to sand with the grain--you may find a circular motion works best. When you are done, wipe off the sanding dust with a rag and apply a second coat of finish. Repeat this step as many times as you wish until you are satisfied with the finish.
For some harder species, like Santos mahogany, you may prefer nothing more than a coat of tung oil. An oil finish will bring out the grain of the wood while sealing it against moisture, but it won't provide much protection against scuffing.
It is not a good idea to finish stairs with lacquer or shellac. These finishes will wear quickly and you will have to remove them completely if you choose to use a more durable finish later.