Let me preface this by saying that you do not have to believe in ghosts, just the possibility of them. That's what I believe that ghosthunters and other paranormal researchers are trying to discover for certain.
I'll go more into theories, equipment and techniques in the future, but here's the basic gist of what we do. This is DCMAG's process: We hear about a possible haunting or are contacted by a client. It's assessed as to how valid it is and a preliminary walk through and interview are arranged. If it's deemed worthy of further investigation we go back again with equipment. We might even visit one or two times more. We analyze the data and follow-up with the client with our findings. Ta. Da.
What are you looking for? Anything out of the ordinary, as well as ordinary things that can create the look of something being extraordinary. You can't be quick to declare everything as being paranormal. You have to apply scientific thought and methodologies to your work, although I think that it should be more of a blend of scientific method and taking into account those unexplained things that go down during investigations.