Construct a balcony in the facade that serves as the wall of the building on your stage set. Use chicken wire to make the balcony shape, and add paper-mache on top of it to give it the look of a solid structure. Make paper-mache paste by mixing three parts water and one part flour. Dip strips of newspaper in the mixture, and lay them across the chicken-wire mold. Attach the balcony to the wall using paper-mache where the edges join the wall structure. This will give the illusion that the balcony actually supports weight.
Add balcony supports. Look carefully at plans for real balconies, note the visible supports' design and recreate them for your set. Include at least two supports that run from the balcony to the wall. Make these out of 2-by-4 lumber pieces covered with paper-mache to match the balcony. Attach lumber pieces to the balcony using paper-mache strips.
Paint the balcony and supports with the same paint you used on the wall. Acrylic paint works best for stage sets, because it has texture. This will add to the illusion that your balcony is solid.
Build a set of stairs behind the wall, out of sight from the audience. These stairs must be solid, like you would find in a house. They must have risers -- the vertical boards that rise to the next step -- as well as treads on the surface of each step. Support the stairs on both sides with stringers -- wood pieces cut to support the risers and treads. Cut these boards in the familiar stair-step shape, and then nail the risers and treads to them. Every three steps, add a post to support the stringers, because these steps must be just as sturdy as real ones.
Build a platform at the top of the stairs out of your panel of plywood. Nail one end of the platform to the top stair, and support the other end with a post. Build it at a height that approximates where the floor of the balcony would be. When the dancer stands on the platform, it will appear she is standing on the balcony floor.
Add handrails for safety. Dancers must move quickly from scene to scene, and handrails will prevent falls. Construct the handrails out of two 2-by-4 pieces of lumber. Make the uprights -- the vertical parts -- of the handrails all the same height, and nail them to the stringers. Use more 2-by-4s for the the tops of the handrails -- nailing them to the uprights.