Latex paint is problematic because it can permanently stain a carpet's fibers if it is allowed to set, which occurs when the paint dries or is exposed to heat. The paint must be damp to be removed from your carpet, because attempting to remove dry paint can damage the carpet's finish. Acrylic paint remover, found at your local hardware store, is safe to use on carpet, and loosens the dried paint to allow easy removal.
Remove as much dry paint as possible from the carpet by gently scraping it.
Pour 1 tbsp. of acrylic paint remover into a lint-free cleaning cloth, and sponge the stain, starting from the edge.
Scrape off the latex paint as it begins to loosen from the carpet.
Blot the stain with glycerin, and allow it to soak into the paint stain for three to four hours.
Mix 1 tbsp. of dish-washing liquid with lukewarm water, and dip a clean cloth into the mixture. Blot the stain with the cloth, and continue blotting with a dry cloth to remove moisture.
Mix 1 tbsp. of white vinegar with 1 liter of water, and sponge the stain.
Blot the spot until all moisture is removed from the carpet.