Size and Prep the Base
Using a miter saw, cut the base of the paper towel holder to size (9-inches-long-by-3¼-inches-wide) from a piece of ½-inch-thick board or scrap plywood. Mark a rectangle 7½-inches-long-by-1¾-inches-wide on the center of the cut board. Using a drill fitted with a 5/8-inch spade bit, drill holes through the board at each corner of the rectangle to create the rounded corners of the opening.
Cut the Opening
Clamp the board to the work surface. Using a jigsaw, cut the line between the holes drilled in step one to complete the rectangular opening.
Set up the Saw
To cut the crown molding flat on a compound miter saw, tilt the bevel of the blade to 33.9-degrees, and then twist the miter angle of the blade to 31.6-degrees. (Note these adjustments are for crown molding with a 52-degree/38-degree molding. If you're working with 45/45 crown molding adjust the bevel to 30-degrees and the miter to 35.46)
Cut the First Piece of Crown Molding
On the bottom edge of the crown molding, mark 3¼-inches from the end of the board. Orient the molding on the saw so that the miter creates a long point at the top edge of the molding and the bevel cuts back into the thickness of the molding.
Finish Cutting the Crown Molding
Finish cutting the molding as shown so that the bottom edge of each piece fits against its corresponding edge of the base board cut in step one.
Cut the Back
Miter the ends of the ½-inch-thick back board to 38-degrees, or the spring angle of the crown molding.
Assemble the Base and Back
Apply wood glue to the edge of the base board. Center the back on the edge of the base, and then nail it into place using a pneumatic nail gun and 1-inch brad nails.
Add the Crown Molding Side
Place the first piece of crown molding along the edge of the base so that it covers the edge of the back board. Apply glue to the edge of the base and the back boards. Nail through the crown and into the base and back boards to hold it in place.
Attach the Front
Apply wood glue to the edge of the installed crown molding piece, and along the front edge of the base board. Place the center piece of crown molding in place, concentrating on the joint with the installed crown. Nail through the crown and into the base board to hold the piece in place.
Attach the Last Side
Glue and secure the remaining piece of crown molding. Add painter's tape across the joints to hold them tight while the glue dries.
Cut and Place the Lid
Cut a piece of ¼-inch board or scrap plywood to a size of 14¼-inches-long-by-6-inches wide. Place the board onto the assembly as a removable cap.