It's a mysterious process never revealed to outsiders, but believed to involve ducks and annotation with hot oil.

For administrators it's easy. You become an Admin by starting a site.

If selecting moderators work on here like it does elsewhere I've been the press is basically the Top Man (or Woman) decides he (or she) want's a new mod and then looks at the members with the requisite qualities and upon finding one who wants to be a mod gives them 'moderator privileges'.
I think, never actually seen it happen myself.