Remove the cabinet door by unscrewing the screws from the hinge with the appropriate screwdriver. Put the screws and hinges in a ziplock bag so you don't misplace them.
Place the cabinet door on a flat surface. Many doors have a wooden insert. Drill a small hole in each corner of the insert. Put the door underneath a jigsaw blade. Insert the jigsaw into one of the drill holes. Cut the inner portion of the wood out by going from drill hole to drill hole in a straight line, leaving the frame intact.
Sand the exposed, just-cut wood on the frame. Apply wood stain that matches the frame to the exposed wood with a paintbrush. Allow to dry. Wipe off excess stain with a soft cloth.
Lay the frosted-glass panel on the inside of the frame of the door. Mark where each glass or mirror holder will be attached with a pencil. Remove the glass panel. Drill holes at the marks and attach the holders to the back of the inside of the frame. Exactly how you do this depends on the type of holder. Follow package directions.
Place the frosted-glass panel on the back of the frame. Slide the holders onto the glass to hold it in place.
Replace the cabinet doors using the screws and hinges from the ziplock bag.