Frame the archway with plywood and 2-by-3-inch framing lumber, or install a prefabricated arch kit. Arch kits are widely available at hardware and home improvement stores.
Use two 1-by-6 pieces of plywood to create the arch. Ensure the curve of the arch comes no closer than 1/5 inch to the top of each panel.
Bend a flexible piece of wood or other sturdy backing into the desired arch shape, and trace the pattern onto the plywood planks.
Cut the arch pattern with a jigsaw, and nail the two arched plywood pieces together using small lengths of 2-by-3-inch lumber. Fasten the 2-by-3-inch braces at 6-inch intervals along the curved arch bottom and straight sides. Arch length and width will vary according to application. The finished frame should be 1 inch shorter than the wall opening.
Cut a length of drywall that matches the length and width of the arched surface, and score it along the back side. Sharper curves will require more cuts.
Hold the drywall in place against the arch. Press the drywall until if conforms to the surface, and secure it with drywall nails or screws.
Apply joint compound and drywall tape, and sand and paint to finish.