How do you get rid of black armpit stains?

You should wash them more often, and do not dry them if the stain remains. Soak them in a mixture of: 1/4 cup bleach and 1/4 cup dishwasher detergent (like Cascade)--you put these into no more than a gallon of hot water in a non-plastic container. Stir so it is mixed completely. Immerse the clothing into the mix and wait about 15 minutes. Then, wash as usual.

You could also try a paste of baking soda mixed with water.