It can seem hopeless but with some time you can get a nail polish stain out of the carpet and next time you are painting your nails put down a towel or don't do it on the carpet.
Test a small area of carpet to make sure the acetone won't melt it. (you can find 100% pure acetone at a beauty supply store, its basically strong nail polish remover)
Step2
Once you're sure it won't ruin your carpet soak the stained area with the acetone.
Step3
Put a towel over the area and press straight down on it as hard as you can. You can set something heavy on it for a few minutes if you want.
Step4
Repeat steps 2 and 3 until stain is gone. It may take more than one bottle of acetone to remove depending on how dark the polish is and how much is on the carpet.
Step5
After the polish is gone clean the area with soap and water to remove the acetone. Set a towel over the area with weight on top to force out the moisture.
Tips & Warnings
Don't rub the stain, this will just spread it around.
Ventilate the area, acetone has pretty strong fumes.