Choose a dresser that is a comfortable height and has ample drawer space. An unfinished piece is suitable. Paint the dresser to match the decor of the nursery, or refinish it if you prefer.
Cut a piece of 1-inch foam to the dimensions of the dresser top. A sharp knife can accomplish this job, but an electric knife works well if you have one. Place the foam on top of the dresser.
Cut the fabric to the dimensions of the dresser top, adding 2 1/2 to 3 inches to each side to accommodate the foam padding. Any fabric that coordinates with the nursery decor is acceptable. A good option is to choose a vinyl or plastic-coated fabric that can stand up to dampness and other accidental messes.
Lay the fabric over the foam so that the edges extend below the top edge of the dresser on all sides. Beginning at the front of the dresser, fold under the raw edge of the fabric so that it becomes even with the edge of the dresser top. Secure with staples along the dresser edge. Continue with the back edge, pulling the fabric tightly across the foam. Proceed to each side, mitering the corners as if wrapping a package.
Cut decorative trim to the length of the front and sides of the dresser, adding 2 inches to the length for wrapping around to the back of the dresser. Glue the trim to the dresser edge, covering the staples. Trim should cover all dresser edges and extend 1 inch onto each side of the back of the dresser. Hold the trim in place until it begins to adhere.