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Soften the paint by soaking it with some hot, soapy water or a stronger solvent. Gently cover the paint with a soapy water mixture made of 1 cup (240 ml) of hot water and 1⁄4–1 teaspoon (1.2–4.9 ml) of mild dish soap. You could also use a solvent such as vinegar, acetone, or WD-40.  Put the soapy water in a spray bottle so you can easily spritz your carpet. Allow the solvent to sit on the paint for approximately 20 minutes. Use a putty knife or some sort of blade to push down into the carpet, and scrape away at the paint. Continue to add your solvent solution and scrape away at the paint. Every once in a while, blot the area with a clean towel to absorb any dissolved and loosened paint.  Remember, try to scrape from the outside of the stain toward the center. You don’t want to spread the paint any further from the spot that is already stained. If there is a lot of paint on your carpet, use a stiff-bristled brush to loosen the paint. If the paint is particularly stubborn, consider using a steam iron to steam the stained area from above. Don’t place the iron on the paint and carpet. Simply hold the iron over the carpet and allow the steam to further loosen the paint.  If steam doesn’t work, use a harsher product like acetone or hydrogen peroxide. Continue to use a putty knife to scrape away at the paint. Use clean paper towels or rags to blot the area dry. You could also lay a few layers of towels or rags over the affected area, place a heavy object on top of the towels, and allow the area to dry overnight. Once the area is completely dried, consider vacuuming the area to pick up any loose pieces of paint either onto of the carpet, or in between the carpet fibers.

Summary:
Saturate and loosen the paint. Scrape at the paint stain. Add steam to the stain. Dry the area.