I'm actually in two homebrew clubs, both of which have annual dues. I think one is $15/year and the other is $25/year. Apart from the usual monthly meetings where people get together to share their homebrew and exchange information, they do fairly regular parties and other gatherings, trips to local breweries, and group brews either on club equipment or at a local brewery.
The regional clubs around here run homebrew competitions, some of which rotate among the clubs and some of which are run by a single club annually.
The more successful homebrew clubs (in terms of membership) around here are associated with the LHBS and have their meetings there. Also, membership in the club gets you a discount at that LHBS.
So far as organization, dues, and the like, you might want to take a look at the information on AHA's website about starting a homebrew club