Although "black box" theatre, in which the actors perform with no props or sets at all, is common among the avant garde, most children's plays look best when performed on a set. Stage scenery need not be expensive or elaborate. Representational scenery is inexpensive and easy to create.
Focus on one set. Most children's plays can be performed on a single set, using costume and lighting changes to denote changes in location. Using one set throughout the play minimises the time needed between scenes and creates a safer environment for child actors, who would otherwise need to stay out of the way of moving set pieces.
Draw a picture. When you read the script, what setting do you envision? Does the story take place in a child's playroom? Is the location a wooded glen? Choose the location and then fill in the details. Are there tall trees? Is there a lake? Draw a quick sketch of the scene as you see it in your imagination.
Use a backdrop. If the theatre has fly rails, you can raise and lower even a heavy backdrop. Otherwise, stretch a piece of muslin on a wooden frame. The backdrop should be nearly as wide as the stage and secured to the floor, ceiling or back wall for safety. Paint the backdrop to represent your chosen location.
Borrow scenery items. Cast members can often provide couches, chairs, tables, inexpensive artwork and similar items. Borrowing as many pieces as possible minimises both time and expense. Never borrow valuable or irreplaceable items.
Build set pieces from inexpensive materials. If properly dressed, plywood boxes can serve as beds, chairs and other furniture items. A folded paper towel makes a convincing wallet. Think outside the box, and remember that the audience will sit several feet from the stage, so props and set pieces need only look convincing from a distance.
Paint everything that will not be covered in fabric. Choose thick latex paint that provides excellent coverage in one coat. Apply a heavy, even coat and allow to dry overnight. Spatter painting keeps painted items from washing out in theatrical lighting. Dip a paint brush in white or silver acrylic paint and flick the brush toward the item. Repeat the process until the piece is evenly covered in specks of paint.
Choose representational set pieces rather than trying to exactly recreate heavy, expensive items. A few plywood trees onstage, and a few painted trees on the backdrop, are sufficient to create a forest. A few books painted on the backdrop can suggest a library. Keep your stage dressing simple and let the audience's imaginations fill in the details.