Screw the three 7 3/4" pieces to the back 32" piece.
Locate your wall studs and transfer the locations to the back piece. Predrill two holes at each stud location and use 3 1/2" wood screws to attach the shelf to the wall.
Add the bottom 1/4" plywood. this piece and the rest of the project will be attached with wood glue and brad nails.
Attach the top 1x10 shelf.
Attach the side 1x4 trim.
Attach the 1x4 front trim. Now you're ready to tape off the walls, sand and finish.