Clear the floor of any obstacles. This includes carpeting, furniture and other pieces of decor. Place all these objects in a separate room, so they don't get in the way or get dirty while you work.
Sweep up any loose debris. Sand away the old finish with an orbital floor sander. Fit the sander with a 60-grit sanding pad, and sand the floor completely. Never let the sander linger on any one spot.
Vacuum the floor to collect the dust, then sand the floor again with a 100-grit sanding pad. Vacuum again, then wipe the floor two or three times with a damp cloth to make sure you collect all the dust.
Apply stain with a cloth. Unlike wood floors, which require you to work with the grain, you should use tight, circular motions to apply stain to a cork floor. Allow the stain to dry completely.
Apply the polyurethane with a foam or lamb's wool applicator. Apply the polyurethane as if it were paint, making uniform strokes all in the same direction. Allow the polyurethane to dry completely.
Scuff the polyurethane with a piece of 220-grit or higher sandpaper. You need only scuff up the surface -- don't remove the finish. Wipe the cork with a damp cloth to remove the dust. Apply two or three more coats of polyurethane using the same method. Allow the polyurethane to dry completely.