This video shot by professional carpet cleaners shows how to remove nail polish from carpet. Unfortunately, most people don't have professional carpet cleaning tools and solution in their home. Nail polish is a difficult stain to remove, but if you act quickly enough you should be able to remove it before it dries. As a professional carpet cleaner in Tampa FL I have dealt with this kind of spills often.
If you get nail polish on your carpet your best bet to get it out is to use Isopropyl alcohol to remove the stain before it dries. Blot up as much of the nail polish with paper towels. If their is still some nail polish on the carpet fibers pour some Isopropyl alcohol on a paper towel and cover the effected area, making sure the alcohol is over the spot. Gently press down to make sure the paper towel makes contact with carpet stain. Leave the paper towel there for 5-10 minutes to break down the nail polish.
With a new fresh paper towel gently blot the area to remove the rest of the nail polish. If any color remains gently blot the area with a dry terry towel to remove excess alcohol and nail polish.
If these steps do not remove the nail polish stain then it's time to bring in a professional carpet cleaner. Make sure the professional you call has experience with nail polish removal.