Prevention is better than curative. Let antiperspirant or deodorant dry completely before putting on your garment. Pre-treat the underarm area of the garment with liquid laundry detergent, so the buildup can be washed away. If the stain is old, treat the area with white or apple cider vinegar to help dissolve the perspiration. Wash in hot water at least every third or fourth time to get rid of the buildup.
Soak in warm water with an enzyme soak product. Wash in warmest water safe for stained fabric. If the stain remains, dampen and sprinkle with meat tenderizer. Let stand 30 minutes to one hour. Rub detergent on stain and rewash.
One thing that is great for whites is natural sunlight, which helps to bleach out stains.