Remove the drapes from the curtain rod, and lay them on top of a thick towel with the paint side facing up. Scrape the excess latex paint off the fabric with the dull edge of a butter knife.
Allow lukewarm, running water to flush the back of the paint stain for several seconds until the water runs clear.
Mix a 50-50 solution of lukewarm water and clear dish soap in a container.
Dampen a clean white cloth in the solution, and blot the latex paint stain for several seconds until you remove the stain. Launder the fabric as you normally would. Continue to the next step if the paint remains on the drapes.
Flip the drapes over, and lay them on a stack of paper towels with the paint stain facing down. Apply dry cleaning solvent to the back of the stain, and let it dry.
Launder the drapes as you normally would, and tumble-dry.