Set up a drum sander with its roughest sandpaper and a dust-collection bag. Run it diagonally to the floorboards so that it smooths the edges of the boards as it takes down the finish. It should take off most of the finish and dig into the wood. Sand the entire floor.
Use a vacuum to take up the dust that hasn't wound up in the dust-collection bag.
Sand the floor again, this time with medium-abrasion paper in the drum sander. Move the sander diagonally in the opposite direction. It should take up the rest of the finish and leave the floor completely bare. Vacuum up the dust.
Sand the floor a third time, loading the sander with the finest sandpaper. Sand in the direction of the boards, getting them smooth and flat. Vacuum thoroughly.
Make a heavy application of maple stain on the floorboards, using a wide finishing brush and beginning opposite the entrance. Brush in the direction of the boards, a few square feet at a time. Let the stain penetrate the maple for about a minute, and then wipe up the excess with rags. Do the whole floor.
Let the stain dry for 24 hours. Wipe up any residual dust with tack cloths. Brush on a layer of polyurethane gloss, starting at the same place and brushing in the direction of the boards. Apply the gloss in a thin, smooth layer. Do the whole floor. Let the polyurethane set for eight hours.
Lightly sand the polyurethane by hand, with extra fine sandpaper, just enough to dull the shine. Wipe up the dust with tack cloths. Apply a second layer of gloss in the same manner as the first. Let it dry, lightly sand it, and apply a third layer. Let the third layer set for 48 hours before using the floor.