Remove any molding around the arched window with a pry bar. Insert the pry bar behind the molding and pull it forward and away from the wall. Some arched windows come with trim manufactured around them. In this case, you may not be able to remove the molding.
Cut along the window's perimeter with a reciprocating saw. This will cut through all of the nails or screws that hold the window in place. If you could not remove the molding from around the window, insert the reciprocating saw blade between the molding and the wall then cut through all of the nails or screws.
Guide the old arched window gently out of the window opening and set it aside. Lift the new arched window into the opening. Place a level on the window's sill. If the arched window has straight sides, use the level to check them for plumb as well. Insert wood shims between the window and the rough opening to raise any low areas.
Drive 2-inch screws through the new arched window's frame and into the opening's framework with a drill equipped with a Phillips head bit. Space the screws 8 to 10 inches apart. Cut off the portion of wood shim that extends past the window with a utility knife.