Cover all upholstery parts of the furniture with plastic tarps. Cut them to fit with a razor knife and tape them along the edges with masking tape. Only the wood parts of the furniture should remain exposed.
Use your vibrating detail sander with medium sandpaper to take off the old finish. Sand with the direction of the wood grain. Brush off the dust.
Reload your sander with fine sandpaper and sand it again, getting the surface smooth and clean. Brush off the dust.
Brush wood stain thickly over the first section of the wood, with a finishing paintbrush. Let it sit on the surface one minute. Wipe up the excess stain with old rags.
Repeat the process for each wood section of the furniture. Let the stain dry 12 hours.
Apply varnish with the paintbrush, in a thin, smooth coat, brushing with the direction of the grain. Let it dry eight hours.
Lightly sand the varnish by hand with fine sandpaper, just enough to dull the varnish. Wipe off the dust.
Brush a second layer of varnish on to the surface. Let it set. Hand-sand it. Brush on a third coat of varnish. Let it set for 24 hours.