Adjust the miter saw to cut at a 45-degree angle by turning the table of the saw until the gauge lines up with the 45-degree mark. Lock the table in place.
Place each 1-by-3-by-6-inch and 1-by-3-by-18-inch board flat on the table of the miter saw one at a time with the 3-inch side resting flat. Cut each end at a 45-degree angle. Make the cuts on the same side on each board so that the boards fit together like a picture frame.
Sand the ends of the boards you cut in Step 2 with a fine-grit sanding block to smooth any rough edges left from using the miter saw.
Place the two 1-by-3-by-6-inch boards parallel to each other on a work surface. Orient the boards vertically lengthwise with the 1-by-6-inch edges resting flat on the work surface. These are the sides of the floating shelf.
Position one 1-by-3-by-18-inch board across each end of the sides to form a rectangular assembly. The 1-by-18-inch edges should rest flat on the work surface. The mitered ends should, again, fit together like a picture frame.
Apply a bead of wood glue to the mitered ends of each board and press them together. Center a frame clamp around the assembly and tighten it. Wipe off any excess glue that seeps out using a damp cloth. Allow the glue to dry for 24 hours and remove the clamp.
Drive trim-head wood screws through the corner joints with a screw gun. Use two evenly spaced screws for each joint.
Position one keyhole slot mount in each corner of the assembly where the 1-by-6 and 1-by-18-inch edges of the boards adjoin on one side. This side is the back side of the assembly. The narrow end of the slot should be facing up. Drive the screws that were included with the mounts through the holes into the edges of the assembly with a screw gun.
Apply wood finish on the floating wooden shelf assembly with a paintbrush. Allow the first coat to dry for four hours and apply a second coat. Wait 24 hours before you mount the shelf to the wall.