Find a food tray, and wash it out well with soap and water.
Trimming to size.
Look for a flat surface, and cut away a piece of styrofoam the size of the print you want to make. Cut away areas that are not flat. With kids, have them use safety scissors.
Draw on the flat shiny side of the styrofoam with a dull pencil. Remember to draw in a mirror image to what you want the final picture to look like. Try not to poke holes in the styrofoam. You should only be pressing on the stamp enough to dent the surface.
Paint over the side of the stamp that you've drawn the picture on. Here I'm using acrylic craft paint. Try not to get much paint in the cracks. If you do, wipe it off with a paper towel, or in the case of water soluble paint, wash it off under the tap, then gently dry.
For a more grown up lithograph look use india ink. Using india ink with children isn't recommended because it stains.
Press the paint side down to the paper.
Carefully lift the styrofoam stamp to reveal the print.
Here's what it looks like if you use more than one color of paint.