Perspiration stains are the easiest of stains to remove using a green cleaner available in your grocery store or drug store. Do not use this method on silk, wool or dry clean only fabrics. Always test a spot first for color fastness.
Buy a fresh bottle of 3% hydrogen peroxide and use it full strength. If you use a 20 to 35% peroxide solution found in some health food stores, then dilute with water 1 part peroxide to 5 to 6 parts water.
Pour the peroxide on the stain and allow to set 30 minutes. Launder in cool water. Air dry to make sure the stain has been completely removed. Repeat if needed. If the shirt has odors as well as stains, then fill a sink with cool water adding 2 cups of peroxide, 1/3 cup food grade distilled white vinegar and a tablespoon of baking soda. Wait 30 minutes and launder.