Vacuum your existing floor thoroughly to remove dust, grime and dirt. Clean your floor with a heavy-duty cleaning agent according to the manufacturer's directions to remove embedded dirt, grease and grime that could prevent the polyurethane from properly adhering to your floor. Rinse your floor with water and the mop to remove all the floor cleaner residue. Allow your floor to dry thoroughly.
Rip several paper bags into pieces of approximately the same size, but don't worry about the shapes -- the more irregular and different, the better. For a leather look, rip small to medium-size pieces about the size of your hand or slightly larger. For a look emulating stone, rip larger-size pieces at least a foot in diameter.
Crumple each piece up in a firm ball to give it a crinkled, aged leather or stone look. Uncrumple each piece gently so they are moderately flat without removing the crinkled texture.
Place a small amount of the water-based polyurethane in the paint tray. Saturate the paint brush with the polyurethane and brush a good amount of it on a small area of your floor. Lay one piece of your crumpled paper on the floor. If you've put enough polyurethane on the floor, the crumpled paper should become saturated. Place more pieces of the paper bag on the area covered in polyurethane so the pieces overlap slightly and completely cover the exposed floor underneath. Work in sections whose breadth is no greater than your arm span, so you can cover an entire polyurethane-covered area without move movement.
Cut off an edge of the paper with scissors or a utility knife when you come to a wall, so an edge of the paper is straight. Lay the paper on the polyurethane-covered floor with the straight edge flat against the wall.
Cover the small section you papered with a thin layer of polyurethane on top of the paper. Apply this coat slowly and carefully, smoothing out the edges of each piece of paper with the paintbrush as you go.
Brush more polyurethane on an adjoining section of the floor. Repeat the paper and polyurethane application until the entire floor is covered. Use a straight pin to pop any air bubbles in the polyurethane. Let the polyurethane dry for at least 24 hours.
Sand down the entire area with the fine-grit sandpaper after the first coat of polyurethane is dry. Apply another thin coat of polyurethane. Repeat this process two more times, sanding in between each coat for a smooth, rich finish.