Draw your building plans to scale. Be sure to label all the important dimensions for your stage construction crew.
Lay out the 4-by-8 sheets of 2 inches thickness extruded foam insulation, available at home improvement stores, on the construction shop floor. Using a felt tip marker and a ruler, carefully draw the cut-lines on the foam sheets.
Cut these cabin parts out of the foam sheets using a "foam knife" made from a hack saw blade or an electric saber saw with a 3-inch blade. Test your parts to make sure they will assemble correctly before continuing.
Prepare a standard or custom-sized stage platform. If the set piece must be mobile, install appropriate casters and brakes on the platform.
Assemble the walls on top of the platform. This process will resemble building a gingerbread house: butter two intersecting edges of foam parts with a bead of construction adhesive. Press the edges together. Thread a small square of two-ply cardboard, about the size of a nickel, onto a 2 to 3 inches long framing nail to form a "cap" on the head end of the nail. Pin the two foam sheets together along the seam, placing a capped nail every 4 to 6 inches along the seam. Set the assembled parts aside to dry for 24 to 48 hours.
Construct an 8 inches high, 3/4-inch plywood "collar" along the interior base of the cabin walls. Use metal angle irons to make the collar stand up perpendicular to the platform surface. Butter the outside face of the collar liberally with a generous bead of construction adhesive.
Move the cabin into the final position on the platform. The inside foot of the cabin walls should meet the outside "buttered" face of the collar. Carefully drill holes through the outside of the cabin walls and through the collar. Use a carriage bolt to bolt the walls to the collar. Space these bolts at every 12 inches.
Assemble a roof, or porch and columns for the cabin in the same manner as the walls. Construct three-dimensional "cabin planks" out of foam and pin these to the walls if desired.
Cover the entire cabin with very light muslin cloth dipped in wallpaper paste. Let this treatment dry thoroughly for 24 to 48 hours. Paint the cabin to suit using latex paint only, because any spray or oil paints may cause erosion to the foam.