You can leave the shower curtain hanging up while you handwash it.
Step 1: Dampen a clean microfibre cloth and sprinkle a layer of baking soda over it. Use the cloth to scrub down the entire curtain, focusing on removing basic grime and dirt, and leaving set-in stains for later.
Step 2: Take a new cloth and dampen it with warm water. Use it to scrub away all of the baking soda and water. You may need to rinse the cloth and repeat to ensure that no traces of baking soda remain.
Step 3: Now’s the time to turn your attention to the tougher stains. Get your cloth damp again and sprinkle it with baking soda, then focus on scrubbing out any set-in stains or mildew.
Step 4: Dampen another clean cloth damp with warm, clean water, and use it to rinse the shower curtain again, taking care to remove all traces of baking soda.