Make a scraper from a piece of stiff cardboard or a section of plastic from a milk container to scoop up the bulk of the fresh paint from the carpet.
Blot up the remainder with a damp sponge until nothing remains but a stain.
Put a few drops of mild detergent in a cup of water, and carefully blot the stain using a clean white cloth dampened in the solution. Rinse the cloth often to prevent re-staining with the soaked-up paint.
Rinse the area with water and another clean cloth until no trace of paint or detergent remains.
Blot the area dry with a clean white towel.
Scrape dried paint with a discarded plastic card or paint scraper if the paint is ordinary tempera or watercolor. These consist of particles suspended in water rather than dyes and become powdery when dry.
Vacuum the remaining powder from the carpet.
Treat any leftover stain as before by scrubbing with a solution of water and liquid detergent.
Rinse and blot dry.
Dampen the affected area with an acrylic paint and varnish remover, then allow the solvent to soak in and soften the paint.
Work on one small area at a time, starting with the outer edges and proceeding toward the center, scraping away the paint as it becomes soft and removing as much as you can.
Rub glycerin into the remaining paint stain, and allow it to soak for several hours or overnight to loosen and gently lift away the smaller bits clinging to the carpet.
Finish by scrubbing, rinsing and blotting. Repeat as necessary until all the paint is gone.