In my own experience (as a researcher, not as a psychic. I have absolutely no psychic abilities at all) people who make claims such as you have are usually either suffering from some form of dissociative mental illness that causes them to lose the ability to distinguish between fantasy and reality, or they are making it up in order to get attention.
In fact, I've never actually come across somebody who claims that they can do what you claim, who actually can do it. Real psychics tend to have a very short range. They often need line of sight with the person\place that they are reading, and many require physical contact (which is why telephone psychics are always bogus).
Nobody really knows how these powers work, though one hypothesis is that there is a higher level of space-time (sometimes known as information space, or similar) that consists purely of information in a raw form (as opposed to our physical universe which consists of matter and energy), and that some people are able to tap into it.
There is no real way to improve a person's ability to read or to have visions other than through practice and meditation. Though hypnotism may help people to make more sense of what they see by removing the bias and interpretations put on visions by the conscious mind.
FYI, people with abilities aren't mutants. They exist at a slightly higher stage of evolution. This is caused by small mutations, but they are natural mutations caused by Darwinian evolution. An actual mutant is somebody who has been changed by an outside force such as exposure to chemicals.
You're confusing real life mutants with comic book mutants.