Measure the height and width of the door opening, going all the way to the outer edge of the frame boards. Subtract 1/2-inch from both measurements and transfer them to a plywood board. Cut out the plywood board with a saw. Sand the cut edges and all the surfaces with fine-grit sandpaper. Wipe down the door board.
Coat the door board with a light coat of stain or paint, applying in smooth, even brushstrokes along the wood grain. Coat the door completely and let it dry for two hours. Recoat and dry until the door matches the rest of the vanity when dry. Apply a coat of sealant and let it dry for two hours. Recoat for three total sealant coats then let the door dry overnight.
Position the door evenly over the frame. Slide two side-mount cabinet hinges between the door and one of the vanity's side boards. Mark the holes in the two boards and drill them out. Attach the hinges in place with 3/4-inch wood screws.
Position a magnetic latch against the other side board of the vanity between it and the door. Mark the holes for the latch and drill them out. Install the latch against the door and the side board with 3/4-inch wood screws.