This is the best homemade playdough recipe I've ever found, compliments of my friend Jan.
You will want to make one full recipe per child who wants to play.
(I usually double the recipe to make two batches at once, using a large Dutch-oven sized soup pot.)
Combine in large saucepan:
1 C. water
1/2 C. salt
1 C. flour
1 T. oil
2 tsp. cream of tartar
Cook over medium heat, stirring constantly, until it forms a solid ball. (This happens quickly, after only about a minute.)
Dump out to cool on waxed paper. Be careful - it will be very hot at first, but it cools quickly. Give it to them while it is still warm, though; this is the best part!
Store in airtight container for repeated use.
You may knead food coloring into the dough when cool, if colors are desired. My kids always prefer the natural color, though, as they are usually pretending in the play kitchen to bake bread, cookies, pizza dough, doughnuts, etc. (Note: playing this way when young easily segues into really baking when one is older!)