Measure a piece of 1-inch by 6-inch lumber back 5-½ inches from the edge and make a pencil mark. Extend the mark across the width of the board, using a square. Note that standard 1-inch by 6-inch lumber is actually 5-½ inches wide, so this measurement will ensure that you have a perfectly square piece when the wood is cut.
Cut along the line with a handsaw or a circular saw. Sand the rough edges of the square piece with 220-grit sandpaper. Round off all the edges of the piece with sandpaper for a smoother look, if desired.
Choose the best-looking side of the square block and place it face down. Make a light pencil mark diagonally from each corner of the block with a straightedge. Drill a hole through the piece at the center where the two diagonal lines meet, using an 1/8-inch drill bit installed in a power drill.
Cut a length of 1-inch-diameter wooden dowel rod to a length of 10 inches. Sand the rough edges with 220-grit sandpaper. Measure across the end of the piece with a measuring tape or ruler to find the center. Drill into the end of the dowel approximately 1 inch with the 1/8-inch drill bit and power drill. Hold the drill straight before drilling to ensure that the hole is not crooked.
Drive a 2-inch wood screw into the hole in the square block from the underside, using a Phillips screwdriver, until a few of the threads protrude from the top side of the block. Apply a layer of wood glue to the end of the dowel where you drilled the hole. Thread the hole in the dowel onto the protruding screw threads of the block. Tighten the screw with the screwdriver until the dowel is tight on the block. Wipe up any glue that may have seeped out, using a damp cloth.
Paint, stain or decorate the toilet paper stand as desired. Allow the finish to dry thoroughly. Place up to two rolls of toilet paper on the stand at a time.