Undo the curtain hooks, and remove them. If you have a curtain liner, wash it separately from the shower curtain.
If the curtain is mildewed, fill a 5-gallon bucket with water, 1/2 cup of baking soda and 1/2 cup of white vinegar. Soak the curtain in the water for at least 8 hours or overnight. Add two white bath towels to the washing machine along with the soaked curtain. Set the washing machine to a setting with two rinse cycles and hot water. Add 1/2-cup chlorine bleach and 1/4 cup of laundry detergent. Remove from the washer immediately, then let the curtain air dry on a clothesline. Repeat for the shower liner, but reduce the amount of bleach to 1/4 cup.
Wear gloves whenever you work with bleach. Dilute bleach in water, then apply it to any remaining mildew stains. Scrub the curtain with a stiff bristle brush using circular motions. Rinse the spots, or wash the curtain again. Let the curtain air dry.