Place the 1-by-12-by-18-inch flat on a work side so that it is oriented vertically. Form the flexible curve ruler into a curve across the top end of the board. Transfer the curve onto the board by tracing the ruler with a pencil.
Set the board flat on the table of a band saw. Guide the board through the saw along the pencil line to cut the curve in the top end of the board.
Drill a hole through the board 1 inch down from the center of the curve in the top end of the board using a 1/4-inch drill bit. This is the mounting hole for the shelf. It can be hung on a nail or screw in a wall.
Set up the table saw with a dado set to cut a 3/4-inch wide by 3/8-inch deep cut in the board. The cut is called a dado and is made by a grouping of blades called a dado set. Measure up 6 inches from the bottom end of the board with a tape measure. Mark the measurement with a pencil.
Cut the dado in the board at the pencil mark by guiding the board through the table saw in a steady manner, moving just fast enough for the blade to cut the wood.
Insert one 1-by-12-inch end of the 1-by-12-by-8-inch board into the dado you cut in Step 5. Drive four evenly spaced screws through the back side of the 1-by-12-by-18-inch board into the 1-by-12-inch end of the 1-by-12-by-8-inch board.
Sand the entire shelf assembly with a fine-grit sanding pad in the same direction as the wood grain until it is completely smooth. Wipe the sanding dust off from the assembly with a tack cloth.
Brush on two even coats of wood finish. Allow the first coat to dry at least 4 hours before you apply the final coat. Wait 24 hours after the final coat before handling.