Strip off the molding or drywall around the doorway in order to expose the framing.
Measure the distance across the top of the doorway, and cut a piece 2-by-3 lumber to fit that length. This is the top plate of the arch frame.
Cut two sheets of half-inch plywood to fit the width of the doorway. Draw an arch on one of the plywood sheets, then cut the plywood along the arch. Lay that onto the second plywood board, and trace the edge of the arch onto the plywood. Cut the second board along the arch. These boards are the arch faces.
Measure the side of the plywood arch face, and cut two 2-by-3 boards 2 inches shorter than that length. These are the side jambs of the framing for the arch.
Nail the jambs to the ends of the top plate to create the outer frame for the arch in the shape of a "U." The top plate will be nailed to the header of the doorway, and the side jambs of the frame will be nailed to the side jambs of the doorway.
Nail one arch face to each side of the wooden framing. Position the faces so that the straight edges are aligned with the 2-by-3 boards in the frame, and the rounded edge is over the open part of the U-shaped frame.
Nail the arch frame to the doorway with the help of an assistant.
Measure the space between the two inner edges of the plywood boards of the arch facing. Cut blocks from 1-by-2 boards to fit this length.
Place the blocks in between the plywood along the rounded edge of the arch frame, and screw them into place with drywall screws.
Cut a strip of quarter-inch drywall to fit along the curved edge of the arch frame.
Dampen the strip of drywall by spraying it with water until you can flex it without causing it to crack.
Screw the damp drywall strip to the 1-by-2 blocks in the arch curve with drywall screws. Use two screws at each block.
Staple flexible corner beads along the bottom edges of the curve every 3 inches.
Spread joint compound over the arch frame with a 12-inch drywall knife. Smooth the joint compound as much as possible, then allow it to dry for the time specified on the packaging.
Cover the arch frame with two more layers of joint compound, allowing each layer to dry.
Sand the surface of the arch framing smooth with fine-grit sandpaper. Wipe the dust off with a tack cloth or a clean, dry rag.
Cover the arch frame with primer and allow it to dry, then apply two coats of paint to the framing, allowing each coat to dry thoroughly.