Measure the space above the door and determine the dimensions of the transom.
Cut the sides of the transom from trim molding that matches the molding of the doorway over which your transom will go. Cut 45-degree angles in the molding using a miter saw, so that the molding will match at the corners.
Glue the trim molding together at the corners to form a frame for the transom. Hold the corners together with clamps as the glue dries. When the glue has dried, staple the corners together at the back, using a staple gun. Fill in any cracks between the joints in the molding with putty.
Paint the molding for the frame and the screen molding, which you will be using later. Use spray paint or a house paint that matches the molding around your doorway. Paint both sides of the frame, so that the mirror placed behind it will reflect the color of the frame and not the color of unfinished wood.
Find a mirror that fits in the hole in the frame but will not show around the outside edge of the frame. Full-length mirrors are good for this. Remove the frame around the mirror, if there is one.
Glue the mirror to the back side of the transom frame, using a strong adhesive. The reflective side of the mirror should face outward.
Cut the screen molding to fit vertically in the frame. The screen molding will serve to divide the frame into panels. Use two or three bars of screen molding, depending on the length of your transom and your own personal preferences. Space the molding evenly across the transom so that the glass is divided into equal panels, then glue the screen molding into place. Use only a little glue to prevent it from leaking out over the sides.
Screw two D-ring hangers into the back of the frame at the top, so you can hang the transom over the doorway.