For the nesting box, start with ripping a 2x4x8′ plank down the center. You need to make two frames as shown below.
Either purchase some 1×2 post or rip another 2x4x8′ plank down the center. Cut as shown and attach to the frame pieces on the inside corners.
Rip pieces of plywood sheet to wrap around three sides. Be sure to measure and layout the cuts to make and be sure they fit flush. Start with the longest sides, cut a rear piece to cover both ends. Attach a handle if you would like.
Cut a dowel to just fit snugly inside the nesting box. Use a rubber mallet or dead-blow hammer to tap the dowel in place just below the top rim of the nesting box. Attach the dowel to plywood with screws through the exterior face of the plywood. Make sure the dowel is BELOW the frame!
Tip the nesting box on its top and cut a piece of plywood to fit the bottom. Attach to the frame with screws. Make sure the bottom is cut to fit (even slightly smaller) so the nesting box will fit in the spaces on the completed coop.
Use a hinge to attach the front piece of plywood to the top, front edge. You will want to attach the hinge to the plywood before attaching the hinge to the nesting box frame. This way you can ensure the nesting box opens and closes properly. Use a hook and eye-pin to lock the nesting box closed.