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Step-by-step build — 5 steps. Also available as a print sheet.
Build the basic 1x3 frame for the shelf — two long rails with the short ribs spaced along the length. The ribs stiffen the shelf and give the plywood skin something to fasten to. This frame is the structure, so make it solid; it's what gets screwed to the wall.
Attach the 1/4" plywood (or MDF) to the bottom of the frame with 3/4" brad nails and glue — 1" nails work too. Keep it aligned to the frame edges.
Cut the plywood front strip to fit and attach it across the front of the shelf with 3/4" nails and glue, covering the frame edge.
Cut and attach the side plywood pieces, then the top skin, wrapping the frame completely. Cut each to fit — a hollow frame rarely finishes exactly nominal.
Fill the few nail holes, sand, and finish. Screw a cleat to the wall studs and slide the shelf over it, fastening from below or behind so nothing shows on top. Confirm it's level before you set the final screws.