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Use a 3/4" round-over bit in your router to trim all four edges of the 1x6 supports.
After routing, cut the supports to 23” lengths.
Test fit the supports in the routed grooves and sand as needed to ensure a close fit.
Go over all flat surfaces of shelves and supports with a random orbital sander for a smooth finish.
Sand the shelf surfaces and edges lightly to eliminate blemishes and marks, but be careful not to sand through the plywood’s surface veneer. Be especially cautious on the mitered corners to keep the edges sharp.
Apply a water-based wood stain with a clean, lint-free cloth. Wipe the stain on in the direction of the grain and rub it in well. Stain the tops, bottoms, and all sides and edges of the shelves.
To get into tight corners, wrap a rag around the point of a screwdriver and use the tip to apply the stain.
Allow the stain to dry according to the product directions, then apply a second coat.
Fill all nail holes with wood putty that matches the stain.
Apply three coats of clear, non-yellowing polyurethane, allowing each coat to dry thoroughly and sanding lightly between coats.
Use a stud finder to locate the wall studs and mark their position with painter’s tape.
Measure the intended height of the bottom shelf, and use a level to transfer that mark across the wall.
Have helpers hold the shelf against the wall on your level line (Image 1), then transfer the stud locations to the cleat along the bottom rear edge of the shelf.
Use a countersink drill bit to bore pilot holes for mounting screws on each of the stud marks. Pre-drill all of the shelves at the same time (Image 2).
Use a power drill/driver and 3" drywall screws to mount each shelf to the wall. Be sure the screws are driven securely into each stud. Provide temporary support with a telescoping pole or other brace until the permanent supports can be installed.
From underneath the bottom shelf, bore 3 evenly spaced 1/4” holes into each of the routed support grooves.
Insert the upright shelf supports into the routed grooves and secure with 1” wood or drywall screws from below.
Measure up 11” from the bottom shelf and drill holes in the upright supports for metal shelf pegs. Place two pegs on each side of the supports to support the middle shelf (Image 3).
Line up the slots routed in the middle shelf with the vertical supports, then lower the shelf down on the supports until it rests on the pegs.
Place the top shelf onto the vertical supports, making sure all the shelf parts are aligned correctly. From above the top shelf, drill 1/4" holes down into the vertical supports, and insert 1” screws to secure the shelf.