Start by reading the literature. Go into the library or a bookstore and read up on paranormal activity. Learn everything you can about ghosts, poltergeists, etc. It should give you some information on how paranormal investigators collect information. You might want to look into joining an organization or a club. Think about taking a class. This will not only give you access to information but also get you connected to the right people. You're probably going to have to buy some equipment after you've learned enough about this stuff.
List of organizations/clubs by state http://funadvice.com/r/3jvnnh3hql
Places that offer classes http://funadvice.com/r/3jvnnh3i0r http://funadvice.com/r/3jvnnh3i4t http://funadvice.com/r/3jvnnh3i8f
Who you gonna call? GHOST BUSTERS! ;)
Paranormal? If you feel that something is happening to you, but you cannot explain it and you are already starting to worry, it is not necessarily ghosts or something else. Perhaps this is a man who does not want you well. in your place I would turn to a private investigator with this question and I think everything would fall into place.
Parapsychology is not a legitimate field of study. To become a paranormal investigator, you do what palm readers and other charlatans do....just claim you are an expert and put together a bunch of hokey illusions to try to fool people into believing you know what you're doing.
I think there is an actual college course called parapsychology... I'm not that informed on it though. Try researching more on it :)