Drill two holes through one end of each 2-inch by 8-inch by 12-inch board. Position the holes up 1 inch from the 8-inch-wide end and 1 inch in from each 12-inch-long side with a drill and countersink bit. These boards will be the sides of your shelf. The holes are located at the bottom end of the sides and will be used to mount the sides to the base.
Place the 2-inch by 8-inch by 24-inch board on a work surface with the 8-inch by 24-inch side flat on the surface. This is the base for the shelf. Butt one side board on each 2-inch by 8-inch end of the base so that the 2-inch by 8-inch end of each side is flat on the work surface. The side with the holes should be oriented on the bottom.
Drive one flush trim wood screw through each hole in the sides into the ends of the base to fasten the shelf together using a screw gun.
Apply wood glue to one end of each plug and insert the glued end into each hole on the shelf assembly. Align the grain of the plug with the grain of the sides. Push the plug firmly into the hole. Allow the glue to dry.
Sand the plug with an orbital sander until it is flush with the surface of the sides.
Apply a wood finish to the fireplace shelf using a poly brush. Allow the finish to dry.