Lay out your foam core board on the floor and sketch the outlines of the scenery you want, such as buildings or bushes. If your scenery takes up multiple sheets of foam core, lay them side by side so you can sketch continuously, but do not attach the foam core together at this point.
Paint your scenery as desired, using acrylic paints. Keep your paints and brushes as dry as possible to prevent the foam core board from warping. Bright primary colors work best for children's theater productions.
Allow the boards to dry completely while lying them flat on the floor. This also minimizes warping.
Cut along the upper edges of your painted area with a mat knife, box cutter or utility knife to remove any foam core you don't want. For example, if your scenic backdrop consists of buildings, cut out the shapes of the buildings to create a skyline. For bushes or trees, cutting around the foliage gives the backdrop an irregular shape that is less distracting than the squared-off board.
Count the number of foam core boards that you have painted.
Mark your 2-by-6-inch lumber into 1-foot segments and use a circular saw to cut two 1-foot segments for each piece of painted foam core. If you have any boards more than 6 feet long, cut three pieces of plywood instead of two for those pieces.
Stand your first piece of foam core upright and place one plywood segment along the back at each end, parallel to your foam core. Set the plywood so the thinner edge lies along the foam core. The wider face should lie along the floor.
Drill a hole through the foam core and into the plywood from the front with an 1/8-inch drill bit. Place a metal washer in front of this hole, and then drive a 1-inch wood screw through it to secure the foam core to the lumber using a Phillips head driver bit.
Drill and secure two screws and washers per plywood segment. The washers help keep the foam core board in place without the screw heads pulling through.
Repeat the process for all of your scenery until each piece has at least two wooden "feet" along the back.
Drill a 1/2-inch hole approximately 3/4 inch deep in the wood "foot" behind any portions of the scenery over 4 feet tall. The hole should be as close to the foam core as possible without splitting the edge of the wood.
Place a dab of wood glue in the hole, then place a 1/2-inch diameter wooden dowel inside the hole to form a vertical support for your scenery.
Add as many dowels as needed to support taller set pieces. Tape the dowels to the back of the foam core with gaffer's tape or screw the foam core into the dowel from the front, using 1/2-inch wood screws.
Dab paint onto your screw heads and washers to blend them in with your scenic painting.
Place the scenery pieces along the stage where you want them to be for the performance.
Place sand bags or stage weights on each "foot" to hold the scenery in place. If your stage allows, you can screw the feet to the floor with 3-inch screws instead of using weights.