If you want to change the shade of your worn-out old polyurethane wood floor, but you don't want to sand it down to bare wood and re-stain it, there is an alternative. While polyurethane is generally transparent, it is also available in tinted form, with stain added to the gloss. The effect is a different shade (whatever shade you want) that's applied in the same way as a new coat of gloss. You still have to screen the old gloss to provide a workable surface, and you should top the tinted polyurethane with clear polyurethane, to seal it.
``Screen'' the floor with your floor polisher and roughest screening disc (60-grit), running the polisher back and forth with the direction of the floorboards and working your way across the room.
Vacuum up the dust.
Repeat steps 1 and 2 with two progressively finer abrasions of screening disc (80-grit and 100-grit). The floor should look flat, dull and clean.
Starting in the furthest corner of the room from the doorway, apply your tinted polyurethane, using a large paint brush. Brush it on in slow, even strokes, going with the direction of the floorboards. Avoid forming bubbles or streaks in the finish. Let the gloss dry overnight.
Hand-sand the dried tinted polyurethane with 220-grit sandpaper. Sand it very lightly, with quick, short strokes, just enough to buff the shine off the surface so the next coat of polyurethane will stick. Vacuum up the dust.
Apply a second coat of tinted polyurethane in the same manner as the first. Let it dry, hand-sand it, and vacuum up the dust.
Apply two coats of clear polyurethane gloss in the same manner as you did the tinted polyurethane, buffing the first coat so that the second coat will stick.
Let the final coat of clear polyurethane cure for two days before using the floor.