Soak a cotton ball with nail polish remover and dab this onto the hair dye stain. Rub gently and you should see the dye begin to lift off your skin. Isopropyl alcohol works in the same way.
Use a non-gel toothpaste on an old toothbrush to scrub at the stain.
Lather up some Lava soap with water and scrub at the stain. This super-scouring soap is good on many stubborn stains, and might just do the trick on hair coloring.
Mix baking soda with enough dishwashing soap to make a paste. Rub this into the hair dye stain and work it in well. Rinse off the paste and your skin should be clean.