This is the classic method that involves a bit of cooking on the stovetop - I prefer it because cooked playdough has a better texture than uncooked varieties. If you want the kids to be able to do it all themselves, try this uncooked playdough recipe.
Warning: Keep away from dogs and other pets. Playdough smells like people food but contains lots of salt, and a hungry dog can eat enough to cause a dangerous salt imbalance.
Step 1: Ingredients
Basic ingredient ratios:
2 cups flour
2 cups warm water
1 cup salt
2 Tablespoons vegetable oil
1 Tablespoon cream of tartar (optional for improved elasticity)
food coloring (liquid, powder, or unsweetened drink mix)