Check the label to see if your curtains are machine washable. If your curtains are thermally backed or have different types of fabric on the lining versus outside do not wash them in the washing machine.
For machine washable curtains: Remove from curtain tracks and remove all hooks. Place in the washing machine (or bathtub if you want to handwash). Add laundry detergent and 1/2 Cup baking soda & wash on a cold wash. Add 1 Cup of white vinegar to the rinse cycle. Remove from machine before spin cycle and hang out to dry.
For fixed blinds such as roman blinds: Vacuum the blind to remove all dust. If you have mould stains kill these by spraying DYC white vinegar onto blind and leaving for 30 minutes. It will not remove the mark but will kill the mould. To remove any left over mould stains mix a solution of detergent and water and blot the mark.