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Locate the wall studs, then attach ledgers to wall at the desired height. Cut the desktop from 3/4"plywood and attach any added features like keyboard tray or ledgers for the legs while desktop is easy to flip and maneuver.
Place the desktop on the wall and measure and cut legs paying attention to cut around any trim that is not removed from walls for a flush fit with the walls. Sand pieces after cutting to make the process easier.Cut legs and secure to ledgers using wood screws and wood glue. When adding a computer shelf, add supports for bottom shelf to the legs. Set in shelf and secure with finish nails and wood glue.
Once the desk is standing with all legs installed and all attachments to the wall ledgers made, trim the edges with wood strips to cover the exposed plywood edge. Secure strips with a finish nailer and wood glue.