Deodorant stains are very common, and just as irritating. A common, but false perception is that it is the sweat that creates these stains, but sweat is colorless. What creates the stains is the aluminum chemicals in the deodorant reacting with the body's natural oils. When you wash the garment and the stains come in contact with detergent, a chemical reaction occurs that can even make the stains worse. And when the stains are there, usually they are there to stay.
If the stains are white and hard, you can use lemon soap and rinse off with room temperature water. Make sure to get all of the soap out, as it can discolor the rest of the garment if there is any left. Never use bleach, as this can make the stains even worse.
The best and most efficient advice is to try and avoid these stains in the first place. You can use deodorant without aluminum salts, not put on your clothes until the deodorant is 100% dry and not use an unnecessary amount of deodorant.