I work for an EHS firm that has Shell, BP, and Conoco as clients and do a lot of site work at drilling sites. I'm usually there in the very beginning, before everything is set up, and don't come back until something goes wrong, but I've met quite a few of these types.
The answer to your question depends on a lot of things. Basically the way it works is that the Well Site Manager is the representative of the company that is paying for the drilling. This would be a company like Shell or BP or whoever. Most everyone else on site is a contractor, whether they're a driller, driver, whatever.
The WSM is responsible for health and safety, project management, and drilling operations. Basically you have a site full of contractors and it's your job to make sure they do what they're supposed to without screwing up.
In my experience, it seems like for the most part you get married to a site. It may be possible to move around a bit, and there may be some scheduling flexibility, but these sites require 24 hour supervision. There may be 2 or 3 WSMs, but one of you will be on site at all times.
The salary and stuff is probably pretty accurate. Even the contractors get paid pretty well.
I can almost guarantee that you won't get hired as a site manager without any experience in project management of any kind. Ideally you'd have experience as a general contractor, clerk of the works, work on a drilling team, or something relevant.
Hope that helps.