Brush down your polyester piece with a dog shedding brush or natural-bristled brush on both sides prior to washing. This will help to remove any loose fibers that could shed while washing or after the piece has been laundered.
Wash your polyester piece according to the temperature and washing instructions which came with it. Use a gentle detergent and pour one cup of vinegar into the wash with it. Vinegar will not only make your piece smell fresh, but will help deter shedding.
Hang polyester outside and let it dry. If it's raining you can dry it in your dryer, but plan to clean out the lint trap halfway through to remove any buildup.
Spray down your polyester liberally with some spray starch and wait two minutes for starch to dry. This will help to make the fibers of the polyester a little stiffer and less susceptible to shedding, without making the piece too stiff.