Take the dresser outside and place it on a layer of cardboard. The cardboard will protect your grass or driveway from staining from the paint.
Remove the dresser fixtures from the dresser with a screwdriver, if desired. You can also leave them on and paint them along with the rest of the piece.
Sand the outside of the dresser with a fine-grade sandpaper. This will remove any glossy finish and give the paint a tacky surface to which it can adhere. Wipe the dresser with a tack cloth when you are done.
Spray the dresser with a coat of spray-on primer. Primers come in several colors, so use the one closest to the finish you want. Hold the can 10 inches from the dresser and spray it on in even, slow strokes. Let it dry according to the primer package directions.
Spray the dresser with the oil rubbed bronze paint in the same way you applied the primer. Use even, slow strokes while holding the nozzle 10 inches from the dresser.
Let the paint dry for 24 hours. Apply an additional coat for a darker look, if desired, and let that coat dry for 24 hours. Replace the fixtures if you removed them.