Measure the space you have available for your cabinet with a measuring tape. A VHS tape measures nearly 8 inches long, so factor that length into the height of each shelf. For example, if you have want a shelf that's 45 inches tall, you have enough space for about five shelves, considering the height of the shelves and tapes.
Plane the edges of two boards with a hand planer, removing any knots or imperfections on the wood. The two boards serve as the sides of your media shelf. Measure out 5-inch sections on a third board of the same size, marking each spot with a pencil. Each board acts as a shelf and holds about 10 tapes per shelf.
Cut the board into 5-inch sections with a saw, following the marks that you made. Rub fine-grit sandpaper over the edges of each piece, or use the planer on the edges. Compare the pieces against each other, making sure that each piece is the same size. Sand or plane the pieces until each is the same width.
Drill four holes with an electric drill in each end of your shelf boards, ensuring they are evenly spaced across the ends. Drill four holes on the bottom edge of each side board, spacing the holes so that they match up with the holes in the shelf pieces. Drill four more holes every 9 inches as you move up.
Lay one of the side boards on a flat surface. Drop a dab of glue in each hole. Insert a wood dowel into each hole. Lightly tap with a hammer. Attach the shelf boards by placing the holes against the dowels and pressing down until the pieces fit together.
Insert wood glue into the exposed holes on each shelf board. Place a wood dowel in each hole. Tap with the hammer. Apply more glue to the holes on your second side board. Line up the holes with the dowels on the shelf. Press down. Clamp the wood pieces. Let dry overnight.
Measure the width of your new shelf. Cut a piece of wood that's wide enough to cover the front. Attach two hinges to the front of the rack. Screw the hinges onto the wood plank with an electric screwdriver. The hinges let the door swing open for access to your tapes.