Cut the lumber into two pieces measuring the depth of your arch and one piece stretching across the width of the doorway. Using two corner brackets, screw the pieces together so that all of the pieces are aligned by width.
Cut the plywood into the width of your frame. Mark the desired diameter of your arch and cut it away. If possible, stack two pieces of plywood atop one another and saw away the excess on both at the same time.
Nail the pieces of plywood onto the frame, opposite one another, making sure that the edges align. Saw away any excess to get the sides even.
Space 1-inch by 2-inch pieces of lumber 2 inches apart along the circumference of the arch, securing each piece with drywall screws on either side.
Soak the drywall in water to allow it to become flexible and fix two layers to the bottom of the arch frame using drywall screws.