When removing paint from a carpet, there are a couple of things that you will have to keep in mind. First off, if you have spilled a whole bucket of paint over your carpet then you need to be realistic about trying to clean it. Do you really think that you are going to get it all off? It is very unlikely that you will succeed. It may be a good time to dig out your insurance policy and see if you are covered for accidental damage in your home.
Another thing that you can keep in mind is that there are different types of paint. Paints fall into two general categories. Water based and oil based. You can tell the difference by the instructions on the container, as to how to clean your brushes. If it says clean your brush in soap and water then this paint is water based. If it says to clean your brush with white spirit, turpentine, methylated spirit or similar solvents then it is oil based.
Within those facts is the clue to the removal of a paint stain. If the paint stain is old and you do not know it's origin then you should treat it as water based and then move on to oil based. It is not going to be a quick job so you need to be patient while you are cleaning.
Water based paint Water based paint comes under many names, emulsion, latex, powder, and many more. First of all, you need to scrape off as much of the excess paint as you can with an old knife or similar type item. Then make a solution of soapy water, using a cup of warm water and a squirt of dish detergent, washing up liquid (Make sure that it does not contain bleach). Using a cloth or sponge - dip it in the solution and dab the stain. Working from the outside in. If the paint does not start to dissolve in the soapy water then you may need to soak the stain for a few minutes. When you have started to dissolve some of the paint then use a tissue to blot up the paint filled fluid that you are creating. You can also use a little clean water to help be sure to get up all the colored paint. The key thing is to always use a blotting motion and not a pouring motion when cleaning up paint spills. You do not want to saturate the carpet and spread the stain any further than it is already.
Oil based paint These will not dissolve with soapy water so instead of using soapy water you will need to use a solvent. As mentioned before solvents include white spirit, turpentine or methylated spirit. A better solvent to use but not essential is dry cleaning solvent on your carpet. Just the same a water based you need to dampen a rag or sponge and dab the paint stain, from the outside in. Not spreading the stain. Then you use a detergent solution to remove the dissolved paint.
You may never get the carpet back to how it was but it is worth a try to save the carpet, lightening the stain so you don't have to live with a bright stain in the middle of the walking area. If paint has been splattered and you just cannot shift small parts then you can snip away some of the fibers from the carpet. But not too much as it will look bald.
If your carpet is of great value then it may be an idea to seek the advice of a professional carpet cleaner as they may have stronger solutions than this.