We are doing Wizard of Oz, which has lots of scene changes. I want to use styrofoam for some set pieces. What is the easiest way for my kids to cut, glue and paint it? I work at in international school in a poor country, so please suggest basic tools and materials as specialized things are not available here.

Using Styrofoam could make your set pieces so light and brittle they might be very UNSTABLE and fragile.  Since basics are the preferred way to go, material-wise and tool-wise, why not use lumber and traditional tooling?  If weight is the issue, take care to design the pieces with minimal (but adequate) substructure to keep the weight down.  You could attach strips of carpet (or if they're available, the Teflon sliders) on the underside of your set pieces to slide them around on (or off) stage.  A clever designer might even design disguised hand holds and leverage amplifiers into the set piece to assist moving/placing them.  Whatever you do, I wish you the best of luck!

I've found a fantastic way to cut the foam is with a fillet knife- gives you sharp, clean cuts.