A friend and I started our local club about 3 years ago. We reserved a room at the library, put an ad in the local (weekly) paper announcing a meeting for people interested in beekeeping, and personally contacted every beekeeper we knew in the area. Had about a dozen show up for that first meeting. We have a membership list of about 50 now, with an average attendence of around 20.
We don't have any formal organization. No agenda, no officers, no dues. We get together and talk about whatever beekeeping problems or issues are on people's minds. We mentor newbees, go to each other's homes to help with inspections, splits or whatever. About once or twice a year we have "planned" meeting with a speaker (such as the State Apiary Inspector) or maybe a class of some kind. We have a Yahoo group mailing list to keep people connected.
On the other hand, there's a new club a couple counties away, and the personality of that club is completely different. They have officers, formal bylaws, take minutes, each meeting has a printed agenda is planned months in advance. They have a professionally done website.
The point is that every group has a distinct personality and you have to adjust and adapt to that. Don't have a lot of preconceived notions about how it should be, just let it develop.