Remove the handles from dresser drawers with a screwdriver. Dab wood putty in the drawer handle holes and push the putty down smooth with a putty knife. Allow it to dry and sand it down smooth with a piece of 120-grit sandpaper.
Run the sandpaper around the entire inner and outer portion of each drawer. Rub them all down with a tack cloth to remove the dust from sanding.
Dip a 3-inch nylon brush in oil-based primer and prime each drawer, inside and out. Allow it to dry. Dip the brush in the paint color of your choice and paint the outside of the drawers one oil-based color. Use a different, but complementary color of paint to color the insides of the drawer. Allow them to air dry.
Measure the length and width of each drawer bottom. Cut a piece of decorative paper to the dimensions of each drawer bottom. Cover the drawer bottoms with decoupage glue using a foam brush and press each piece of paper onto the sticky bottom. Smooth it out using the edge of a credit card.
Stack the drawers against a wall on their sides on top of each other, with their inner portions facing outward. Drill a drywall screw into each drawer, inserting the screw through the drawer bottom.