Go over the floor with your hammer and centerpunch, section by section, knocking down any raised nail heads.
Set your heavy sandpaper onto the floor sander. Run the sander over the floor's surface from one side of the floor to the other, moving with the direction of the floorboards. Work your way across the room course by course, taking up most of the existing finish. Vacuum up the dust.
Sand the floor a second time, using the medium sandpaper in the sander, to take up the last of the old finish and completely expose the wood. Vacuum the floor. Sand a third time with fine sandpaper in the sander to get the surface smooth and clean. Vacuum thoroughly.
Use a paintbrush to apply wood stain to the floor, starting in the far corner from the doorway and working in sections of about 4 square feet. Brush the stain heavily onto the boards, let it sit for a minute and then wipe up the residual stain with rags. Do the entire floor.
Let the stain set for 24 hours. Run tack cloths over the whole floor to take up any remaining dust.
Apply polyurethane floor gloss over the floor with a paintbrush, in a thin, flat layer, with the direction of the floorboards. Do the whole floor. Let it dry for six hours.
Lightly sand the dried polyurethane by hand with extra-fine sandpaper; sand just enough to dull the shine. Wipe it down with tack cloths to take up the dust.
Apply a second coat of polyurethane in the same manner as the first. Let it dry six hours. Dull the shine with extra-fine sandpaper. Wipe up the dust. Brush on a third layer of polyurethane. Let it set for 24 hours.