Wipe down the dresser with a clean tack cloth or cheesecloth. Working first on the horizontal surface, drizzle a light line of polyurethane onto the dresser. Spread in the direction of the grain using a bristle brush, working quickly and brushing over the same area only as much as needed to avoid bubbles, streaks, or imperfections. Cover the entire dresser. Let dry completely, about 12 to 24 hours.
If a second coat of polyurethane is desired or imperfections appear, lightly sand with very fine grit sandpaper; wipe with a tack or cheesecloth. Repeat the polyurethane process. While the polyurethane dries, spray-paint the hardware. Allow to dry completely, then reinstall.