Build a frame for the arch by cutting 2-by-3-by-96-inch lumber into three pieces equal pieces. Two will line the sides of the doorway and one will line the top. These dimensions will vary with the size of your door and the desired depth of your arch. Secure the three pieces accordingly into the frame using 2-inch nails.
Draw the arch you want on a large piece of cardboard and use this as a template to cut out two arches from the 1/2-inch plywood. These arches can be drawn freehand, though this will likely produce an uneven edge. For a more exact edge, use a protractor or trace around a circular object with a radius that matches that of your intended arch.
Position the plywood pieces on the three lumber pieces, ensuring they are flush. Screw them into place using 2-inch screws.
Attach the lumber blocks to the inner radius of the arch with drywall screws, spaced 2 inches apart. They should fit the width of the opening. Trim any excess with a saw.
Cut a drywall strip that measures the width of the arch frame and long enough to run the length of the arch. Place the drywall completely in water and allow it to soak for an hour so that it can bend into the shape of the arch.
Nail the drywall into the lumber blocks using drywall screws spaced 6 inches apart.
Cut a piece of drywall to fit over both plywood arches, and cover the arches with it. Cut off any excess with a utility knife.
Mix joint compound and apply to the doorway, covering the arch completely. Allow the arch to dry.
Sand the arch with 150-grit sandpaper and paint it to your liking.