Run a bead of construction adhesive around the back perimeter of the birch plywood 2 inches from the edge. Run two beads of adhesive spaced evenly down the center of the panel on the back.
Stand the birch panel on the floor, flat against the wall. Press it against the wall to smash the glue flat. Shoot pin nails around the perimeter of the plywood space 12 inches apart.
Shoot two pin nails into the center of the plywood 12 inches apart approximately where you ran the beads of adhesive on the back.
Run a bead of adhesive down the center of the 1/4-by-4-by-96-inch piece of alder. Lay it on its side on the floor flat against the panel flush with the edges. Use the pin nailer to shoot pin nails through the alder every 12 inches to attach it to the panel.
Make light pencil marks on the top edge of the alder at 16, 32, 48, 64 and 80 inches with a tape measure. Run beads of glue down the center on the backs of the five 1/4-by-4-by-28-inch pieces of alder. Stand them centered on the marks on the edge of the 96-inch piece of alder. Shoot four pin nails evenly spaced into the center of all four pieces to attach them to the panel.
Run a bead of glue down the backs of the two 1/2-by-4-by-36-inch pieces of alder. Stand them at the ends of the panel. Shoot four pin nails through the center of each of the pieces spaced at 12 inches to attach them to the wall.
Run a bead of adhesive down the back of the 1/4-by-4-by-96-inch piece of alder. Place it on the panel on top of the 28-inch pieces of alder. It should fit snugly between the two outside pieces. Shoot pin nails through the center, spaced at 12 inches to attach it to the wall.
Putty all the nail holes with wood dough and a putty knife. Sand lightly with 120-grit sandpaper.