Answer:
Use gel coloring, not the liquid colors you can buy at the supermarket. Knead the fondant to soften it, then add the color and knead it in until it's thoroughly mixed. Some colors will deepen overnight, like Americolor's super red and super black.
If you are making the fondant and need an entire batch of one color, it's easiest to add the color when you add the liquids to the recipe.
If you're making black fondant and don't mind it having a chocolate taste, substitute 3/4 cup cocoa powder for 1 cup of powdered sugar in your recipe, and you'll end up with dark brown fondant. Add a tiny bit of black color and let it rest overnight, and it will turn a nice dark black.