Measure the length, height and depth of the space where you want to install the countertop bath tower with a measuring tape. The height of the tower should be less than the distance between the countertop and the ceiling, and its length should not interfere with accessing the sink.
Cut two pieces of 1/2-inch hardwood to the length and depth of the bath tower with a circular saw. These two boards are the top and bottom panels. Cut two more pieces of 1/2-inch hardwood to the depth of the tower and the height measurement, minus one inch, for the side panels.
Stand the four pieces of 1/2-inch hardwood you just cut upright on their longest 1/2-inch edges. Arrange these boards in a rectangular shape and insert the side panels between the ends of the top and bottom panels. Drive 1-inch wood screws through the ends of the top and bottom panels into the side panels to complete the frame.
Use the circular saw to cut a piece of 1/2-inch hardwood for the back panel. Subtract 1 inch from both the length and height measurements of the bath tower and use these dimensions to cut the back panel.
Lay the rectangular frame on the ground and place the back panel inside so it lies flat on the floor. The four edges of the back panel should be flush with the inside edges of the rectangular frame. Drive 1-inch wood screws through the top, bottom and side panels into the back panel to secure it.
Measure and mark the position of any shelves you want to add to the bath tower along the side panels in pencil. You may choose to install shelves at even intervals or vary the shelf height to accommodate the storage of a variety of items.
Subtract 1/2-inch from the depth of the bath tower and 1 inch from its length to find the dimensions of the shelves. Cut the shelves out of 1/2-inch hardwood with the circular saw.
Slide the shelves horizontally into place between the two side panels of the bath tower frame where you made the pencil marks. Use a level to ensure each shelf lays flat. Drive 1-inch wood screws through the side and back panels into the shelves to attach them.
Paint or stain the finished countertop bath tower to match the decorating scheme in your bathroom. You may want to apply a coat of clear varnish or polyurethane to protect the surface of the tower from water damage.
Set the countertop bath tower upright in the desired location on top of your counter. If the tower appears to be sturdy enough on its own, you may leave it as a stand-alone piece. If desired, screw one side of a metal wall bracket onto the left and right side panels and screw the other side into the wall to support the bath tower.