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)
Step 2: Mix and heat
When the dough pulls away from the sides and clumps in the center, as shown below, remove the pan from heat and allow the dough to cool enough to handle.
IMPORTANT NOTE: if your playdough is still sticky, you simply need to cook it longer!
Keep stirring and cooking until the dough is dry and feels like playdough.
I've gotten many comments asking about sticky dough, so please just keep cooking a bit longer and it will work!
Step 3: Knead & color
Make a divot in the center of the ball, and drop some food coloring1 in. Fold the dough over, working the food color through the body of the playdough, trying to keep the raw dye away from your hands and the counter. You could use gloves or plastic wrap at this stage to keep your hands clean- only the concentrated dye will color your skin, so as soon as it's worked in bare hands are fine.
Work the dye through, adding more as necessary to achieve your chosen color.
1 If you use unsweetened drink mix for color, test on a small ball first- it won't go as far as the "real" food coloring.
Step 4: Play and store
When you're done, store your playdough in an air-tight container.
- If it begins to dry out, you can knead a bit of water in again to soften the dough back to useability. Once it's dried past a certain point, however, you'll just have to start over; thankfully it's not terribly difficult.
- If it gets soggy, you can re-heat it to drive off the extra water the dough absorbed overnight. This is usually the result of high humidity, but is fixable!
You can also bake it in the oven to make hard dough figures and ornaments, then paint or otherwise decorate the surface. One of the comments below even suggests using baked play-dough as a salt lick for your pet rabbit! (thanks, redcore4!)