Measure the inner edge of the door frame. Using these measurements, cut enough half inch thick lumber for the top, bottom, side and cross pieces for top and base frames. Glue the base frame together so the pieces fit squarely flush together. Glue the top frame onto the base frame. Toenail the cross pieces to the side pieces of the door. Staple the screen mesh onto the base frame. Add trim to the frame to hide the staples.
Before gluing the door frames together, lay the pieces out. Trim with a handsaw or pare it down with a chisel to ensure a tight fit. Glue the top frame onto the base frame so that the outer edges of the two frames are even with one another. The horizontal pieces of the frames should overlap, fitting solidly together to strengthen the door.
To avoid splintering, pre-drill the toenail holes on the cross pieces. After stapling the screen mesh onto the base frame, use a utility knife to trim away any excess screen mesh. For added stability, install diagonal cross braces. Measure the angle of two opposing inner corners of the frame. Mark another piece of wood with this and cut along the marks. Fit this into the frame then fasten with nails, screws or pins.