To allow your handle-less closet door to remain shut, you will want to install a closet door ball catch. Closet door ball catches come in many sizes and finishes. Choose the one that matches the style of your home.
Step 1: Install the Ball Tube
Line up the ball tube and mark where you want it on the top of the door. Make pencil marks where any screws will go. Some of the closet ball catches are simply sunk into the door with wood glue, others will require screws to hold it. A third type just screws into the wood itself. If the piece has screws, use a drill bit, just slightly larger than the ball tube, drill a hole deep enough to take the ball tube. Mark screw holes with the pencil and use a bit smaller than the screws to start a hole to prevent the wood from splitting. Fasten the ball in place using the power drill and screwdriver tip.
Step 2: Prepare the Door Jamb
With the pencil, place a small pencil mark on the inside of the door, corresponding with the center of the ball. Shut the door and continue the mark to the door jamb. Open the door again and mark across the jamb. Measure the offset from the side of the door to the ball center and mark across the line on the jamb. This will mark the center of the indentation on the catch plate. Center and mark where the catch plate will lay on the door jamb. With the chisel, whittle out the length of the catch plate so the plate will lay flush with the jamb.
Step 3: Install the Catch Plate
Place the plate on the door jamb, mark, drill the screw holes, and attach the plate.