There are a million different play dough/clay recipes out there. This is the one we like. I make four batches, one for each primary color of red, blue, and yellow and one which remains white for lightening shades. From there any color can be made by mixing the finished clays together. The home-made clay is so far superior to the store-bought type that it's hard to make a comparison. The home-made clay doesn't dry out nearly as quickly nor does it have that strange smell.
1/2 cup salt (I use kosher since it's so cheap)
1 cup flour
1 T cream of tartar
1 T oil
1 cup water
plenty of food coloring
Add all ingredients into a saucepan and cook over low/medium heat until the dough pulls away from the sides.
note: I've read so many recipes which call for just a few drops of food coloring. In my experience it takes a good half of a small bottle to get really nice vivid colors. The first time I made it I added only a few drops at a time, save yourself time and just dump it in. Allow to cool then knead for a few minutes. So easy!