My job title is technically "researcher," and I know people who do it variety of ways, so I'll take a stab at this in a general sense. I don't know anything about historical research, per se, but lots of industries/businesses hire people to do research. Obviously, there are universities and their associated research centers, but outside of academia you have consulting firms (my industry), politicians and political groups, law firms and legal groups, journalism (all varieties), scientifc labs, etc.
Pure historical research is probably quite rare, I'd imagine, outside of academia. If you're thinking of freelancing, I really don't know. As for pay, people will only pay you to research if they're going to make money off your work, and your pay will be dependent on how much money someone thinks they can make off of you.
Some industries pay well, others pay very poorly. Usually anything associated with the humanities, like history, falls at the lower end of the scale - sadly.
Everyone I know who does or has done research for a living has advanced degrees of some sort, or specialized degrees in their area of research. (e.g. I have a doctorate in psychology, but I do educational evaluation. An ex of mine did a dual major in journalism and science, and so became the science researcher for a health magazine before being promoted to writer.)
I have no idea if that was helpful, but good luck!