Position the mirror on the door where you plan to install it. Use a carpenter's level to ensure that the mirror is positioned plumb and level. Trace a line on the door to mark the position of the bottom of the mirror. Mark the positions of the lower corners of the mirror on the door. Remove the mirror and set it aside.
Mark a line on the door 2 inches from either end. Use an awl or a nail and hammer to make a 1/4-inch-deep pilot hole through each mark. Pass the tip of a screw through one mirror clip. Insert the tip of the screw in the pilot hole. Turn the screw clockwise with a screwdriver to tighten it. Install the second mirror clip in the opposite pilot hole.
Position the mirror on the door so the lower clips support the mirror. Use a long piece of masking tape to temporarily hold the upper portion of the mirror in place as you install the upper mirror clips. While this step is not strictly necessary, it makes the job easier.
Measure and mark the door 2 inches from the upper outer corners of the mirror so the upper mirror clips will be aligned with the lower clips. Place the mirror clips on the upper edge of the mirror, aligned with the marks on the door. Pass the tip of the awl or nail through the screw hole in one mirror clip. Tap the awl or nail to make a pilot hole in the door. Repeat to make a pilot hole for the clip on the opposite end of the mirror.
Screw the upper mirror clips in place. Remove the masking tape to complete the project.