Lay out newspapers under and around the piece of furniture.
Use a detail sander and rough sandpaper to take off the existing finish, sanding it down to bare wood. Wipe off the dust.
Sand it again, this time with fine sandpaper, to smooth out the surface. Clean up the dust.
Put on rubber gloves. Brush wood stain on the surface, starting at the highest point and working in sections of a few square feet. For each section, brush the stain heavily on the surface, let it sit for a minute, and then wipe off the excess with a rag. Do the whole piece.
Let the stain dry for 24 hours.
Brush polyurethane over the surface with a paintbrush, starting at the top and brushing with the grain of the wood. Apply it in a thin, even layer. Let it dry for six to eight hours.
Sand the polyurethane with extra-fine sandpaper, by hand, just enough to dull the gloss. Wipe off the dust.
Apply a second layer of polyurethane in the same manner as the first. Let it dry, dull the surface with extra-fine sandpaper, and apply a third layer. Let it dry overnight.