Most paint is made to be permanent, so it's no surprise that it's hard to remove from carpet. Even though there are some chemicals that will break down paint rather easily, the big problem is that those same chemicals will break down the glue that hold the strands of carpet fibers to the backing of the carpet. One trick is to never apply the chemicals directly to the carpet, put it onto a rag, and then apply. Now if you catch a paint spill, remove it right away. The effort it takes to get wet paint out of carpet is nothing compared to the hard work it takes to try and fix the same problem after the paint has dried, if it's possible to fix at all. Here is a common ring of dried paint left on carpet that has had a drippy paint can left on it.
After a little work things are starting to look a lot better. This carpet couldn't be restored to it's pre-paint accident condition but the improvement is significant.
The owner and the person who left the paint on the carpet were both very pleased.