In a pot, add vegetable oil, water and then add the food coloring. Stir until they are mixed well.
Then add in the dry ingredients. Add the salt and cream of tartar and mix until they are both dissolved in the liquid.
Slowly add in the flour and mix well (it will be runny and gooey).
Now turn the heat up to medium heat on the stove and continue to stir the mixture until it is thick. It will start to stick to your spoon or spatula, whichever you are using to mix it. Once the dough starts to form a ball as you mix it, remove from the heat.
"Plop" the mixture into a large mixing bowl and allow it to cool.
Once it is cool to the touch, knead the playdough to get it nice and soft. This is when I like to get the kids involved. Playdough works best if it is kneaded for roughly 10 minutes after it has cooled, the kids have no problems playing with playdough for that long, so it is perfect!
If you have little kids then you can stick the playdough into a ziplock bag and have them knead it that way, but I have always found they take it out of the bag any way so I don't bother with them.
If your playdough is a little sticky you can add a SMALL amount of flour to it when you are kneading it.
Once you are done kneading your playdough, you can play with it immediatly or store it in an airtight container or ziplock bags.