Rest the Broadway flat on its back. Measure the height of the hinges. Adjust your router to compensate the depth the hinge will sit within the face of your Broadway flat. Loosen the clamp inside the router's base and move the motor housing up or down until you reach your desired depth. Measure the length and width of your hinge, add to those lengths the diameter of your router base.
Cut a rectangular piece of formed hardboard sheeting on a band saw. Cut it into a C-shaped frame within which you will route the depth into the side of the flat for the hinge. It should look like a rectangular frame with one of the long sides removed. "C-clamp the formed hardboard sheeting onto the side of the flat where you want to have your first hinge," advises "Backstage Handbook" author Paul Carter. "It is recommended that you make them evenly-spaced along the side of the flat, dividing the side into thirds or fourths." Make sure that the formed hardboard sheeting guide is in place and that you perfectly route the area needed for implanting the hinge into the face of the flat. This can be done by simply drawing an outline of the hinge and--with the router bit up--tracing along the side of the flat with the router and observing whether or not the router will route the area necessary for the hinge. Route three or four evenly-spaced positions for the hinges.
Put the hinges in place and drill the hinge down through the two pieces of one-by. Stand the flat up. Apply wallpaper or canvas over the hinges to hide them if you wish.