If you need to remove paint from carpet, there are several methods that may work.
Just a drop of paint:
If you have spilled just one tiny drop of paint on your carpet, simply let the drop dry then use scissors or a razor blade to cut that one strand of carpet and remove the drop. If you try to remove the paint from your carpet, you risk staining the adjacent strands and causing extra unnecessary work.
A little latex paint that is still wet:
If you have just spilled a little latex paint on your carpet and the paint is still wet, first try absorbing as much paint as you can in a disposable cloth or paper towel. Do not rub or smear the paint because that will make the stain worse. You may want to use a knife as a boundary to keep the paint from spreading to other carpet fibers. Once you have removed as much of the paint as you can, use laundry soap and water to scrub the spot over and over again to remove as much of the paint as possible. You may also want to try using vinegar to remove the paint stain. A wet vacuum may help.
Lots of latex paint that is still wet:
If you have spilled a whole can of latex paint on your carpet, first absorb as much of the paint up as possible using a disposable towel or rag. Drench the spot with water and absorb the water with a wet vacuum. Continue this process over and over. Once most of the paint has been absorbed, use a scrub brush with water and laundry detergent to get all of the paint out. You may have to pull up the carpet to make sure all of the stain is removed and to make sure the carpet dries properly.
Dry latex paint:
If you spilled latex paint and it has dried, first try scraping up the dried paint with a knife. After you have removed as much of the paint as possible, follow the steps above for removing wet paint. If the paint will still not come out, you can try acetone, paint thinner, or hydrogen peroxide, however they may change the color of you carpet.
Wet oil based paint:
If you have spilled oil based paint on your carpet and it is still wet, get a disposable rag or cloth and absorb as much of the paint as possible. Once you have absorbed as much paint as possible, use mineral spirits, acetone, or lacquer thinner to try to get the paint out of the carpet. Put the chemicals on clean rags and use the rags to get the paint out of the carpet. Please note that these chemicals may discolor your carpet.
Dry oil based paint:
If you have oil based paint that has dried on your carpet, most chemicals will not be able to remove the paint. Try using a very hot steam cleaner to try and detach the paint from the carpet strands. This will be a very time consuming and tedious process.
If you have tried all methods and nothing seems to work, you can try patching the carpet. If you have a closet or small room with the same carpet, you can use the carpet from that area to patch the area with the paint stain. You should probably hire a carpet professional to make sure the carpet will be rotated, seemed, and stretched appropriately so the patch is not visible.
Please be aware that some methods for removing paint from carpet run a chance of discoloring your carpet, so make sure to check for color fastness in another location that is not very visible before proceeding.