Some brands of air-dry clay can be purchased pre-colored, but many are available as white (or off-white) only. These can be pre-tinted or painted after curing. Just about anything that has pigment in it can be used to pre-tint air-dry clays. That includes acrylic paints, oil paints, pigment powders, pastel chalks, food coloring pastes and similar products. Just add a little color into some clay and knead until mixed in. It may sound like extra work, but it's actually quite handy to be able to mix your own colors as needed.
The strongest colors (such as a deep red) are best achieved with artist quality paints (oil or acrylic) because they have more pigment than craft paints. I personally prefer to use the food colorants that are available in paste or gel form such as those available from Wilton. That's just because I find them less messy. These colorants are usually found in a cake supply store or you can find them at Amazon.com.
Even pre-colored clays need to be combined at times to get the optimum color. The color chart from Rainbow Clay shown above is helpful when mixing various colors of pre-tinted clays to get your own custom colors. It may also help you figure out which colors to mix when pre-tinting. See our page "Paint or Pre-Tint" for more information about tinting clay.