Clean your shower curtain by sprinkling baking soda on a sponge and scrubbing. Rinse well. A mildew stain on the curtain can be tackled by briskly rubbing in a baking soda and water paste. When a shower curtain really needs help, remove it and wash on the delicate/cold cycle of your washing machine, adding vinegar and baking soda as the only detergent. Add a bath towel to help agitate the grime off. To prevent mildew from coming back, add another cup of vinegar to the final rinse cycle.
You can practice preventative maintenance here as well by keeping a spray bottle of vinegar and water in your shower. After each shower, spray down the shower curtain or doors to prevent scum and mineral buildup. Another old-fashioned tip for mildew prevention is to soak the curtains in salt water. This can be done right in the bathtub: Fill it with warm water and pour in 1/2 cup salt as it fills. Drop the curtains right into the tub to soak, then hang up to drip dry.