Remove the door at the hinges if there is one in place.
Run a utility knife in between the trim and the wall to cut away the paint and caulking around the door trim. Insert a flat pry bar into the gap and loosen the trim so it can be pulled off the wall.
Remove doorjambs and baseboard molding. Carefully insert the claw end of a hammer in between the wall and the molding, and gently pry it away without damaging the wall.
Cut two pieces of 1-by-4 to a length of 8-inches, and cut another two pieces one-third the width of the opening to create nailing blocks for the new drywall. Nail these four pieces to the top corners of the opening, fixing the 8-inch pieces to the side of the opening and the longer pieces to the header at the top -- each should form an "L" along each top corner.
Cut two pieces of drywall and a piece of cardboard to a height of 15 inches and to the same width as the opening. Screw the drywall to the nailing blocks on each side of the door frame.
Lay out the cardboard and create a template for the arch. Draw an arc from one end of the cardboard to the other with its high point dead center. Ensure your arch is perfectly symmetrical and cut out the arched center piece -- this is the template. If you are using a kit, the arch template is included. Position the arch template against each drywall piece, draw around it and cut out the shape with a drywall saw.
Apply adhesive-backed fiberglass mesh tape to the seams between the wall and the new pieces of drywall. Apply joint compound over the mesh tape, using a brush to apply up to three coats. Allow to dry, sand smooth and apply a coat of primer.
Push the prefabricated archway -- it is usually has a curved piece to cover the gap between the drywall and decorative trim for the front and back faces -- into place, pushing it upwards as far as it will go. If necessary, ask someone to hold it in place momentarily. Position the two column parts that often come with the kit, or your own casing, cut to the proper height, on either side of the opening, underneath the arch and slip them onto the wall. Ensure everything is square and snug, and that the arch meets the column s in the correct way, then nail into place using 2 1/2-inch finishing nails.
Paint the new drywall with paint to match your existing wall and the new arch and column casing with trim paint to finish.