Move the dresser to an area with plenty of space and adequate ventilation. Spread a tarp or drop cloth under it to protect the underlying surface. Remove all of the drawers and set them alongside the dresser on top of the tarp.
Remove the knobs or handles from the drawers by removing the screws located on the inside of the drawer. Place the hardware inside a plastic sandwich bag and set it in a safe location.
Don a dust mask and safety goggles and sand the entire surface of the dresser with a fine-grit sandpaper. Do not attempt to remove the finish, simply scuff it to create a dull finish, which accepts paint better.
Wipe down the dresser using a tack cloth to remove all sanding dust from it.
Remove the top cap from a can of spray primer and shake it up for 10 seconds. Apply an even coat over all exposed surfaces of the dresser and the drawers. Allow the primer to dry for two hours. Then turn the drawers and prime the bottom sides.
Wait another two hours and apply a white, interior latex-based paint using a paint roller. You may want to use a small trim size roller to reach tight spaces. Allow the paint to dry completely and then apply a second coat, using a paint brush when needed to get into intricate scroll work or patterns.
Allow the paint to dry overnight or until it is no longer sticky when touched. Re-attach all of the knobs or handles using the screwdriver.