Major tip: buy ingredients (especially cream of tartar) at Bulk Barn, wayyyy cheaper than the grocery store.
Ingredients (single batch):
Combine water, salt and cream of tartar in a saucepan. Cook on low heat, stir with a wooden spoon. Stir in the oil, then the flour. Keep stirring until the mixture starts looking dry and pulling away from the sides of the pan. Remove the pan from the heat at this point. Pinch a piece between two fingers. If it is not sticky, it is done. Place the dough on the counter and knead until smooth. Careful, it's HOT! at first. Add colour at any point in this process, or later.
Giant Recipe: Increase the quantities, it works just as well.
Prepare as above.
I often make the giant batch and divide it up to make a zillion different colours. It keeps very well in a sealed ziploc bag in the fridge or container. You can also add glitter, scents (cinnamon, vanilla), etc. after the dough has cooled.
Some of our momstown chapters have Playdough & Popcorn parties! fun fun!