This is information taken from the experiences of people who are members of fan clubs, and other fans. Take it with a grain of salt. If you have any corrections or see anything you disagree with, let us know.
Fan clubs: how-to, privileges, and responsibilities
Tomo no Kai
The only official Takarazuka fan club is the Takarazuka Tomo no Kai. Literally meaning the "Takarazuka Friends Club," the website for this organization is here on the official Hankyu website.
Tomo no Kai is not a fanclub for an individual seito, but for the company as a whole. The club offers ticket sales for all troupes to its members before the general public, and also hosts special talk shows with prominent or rising stars.
Membership is only open to residents of Japan, because of the requirement of a Japanese bank account.
Individual Actresses' Clubs
Besides Tomo no Kai, a number of theoretically unofficial fanclubs for individual actresses do exist and command a significant amount of influence. The most visible marker of this influence is in how the staff run iri-demachi at the stage door. Behind the scenes they will also organize the fans into buying tickets to performances and hosting tea parties for their actress, among many other things.
There are obvious benefits to being in a fan club. Particularly in smaller clubs, you may have opportunities to speak with or hand over your letters and presents personally to the actress you support. The club provides updates on public appearances and publications, ticket forms for performances, ochakai (tea parties) and dinner shows, and often order forms for club-exclusive merchandise.
Being in a fan club is also expensive. There is a fee to apply, and then a yearly fee thereafter, which goes towards buying presents for the star and toward organizing things like ochakai, etc. Among many written and unwritten rules are the following: You may join only one club and attend iri-demachi only for that actress. Photo-taking at iri-demachi is forbidden. In Tokyo, you must wait until all the stars have left before the club disperses. While the rules vary by troupe and even by club, in general they are strict and may seem stifling.
Takarazuka clubs generally do not have publicly accessible web presences. Joining is pretty much limited to contacting fan club staff in person at iri-demachi or ticket distribution times, or contacting the actress herself through the mail. Clubs may or may not permit foreign members, and may or may not place additional restrictions on you. If you are allowed to join, you'll receive a form to mail in, and instructions on how to wire your dues to the club. Bank-transfer is often difficult (or impossible) from outside of Japan, so prepare to make arrangements with a Japanese contact or cause a great deal of trouble for your club.
All the same, many clubs are happy to have anyone who genuinely admires their star and they can be a great deal of fun.
If you would like to read a description of fan clubs from the point of view of a Japanese fan, please refer to the first part of Takarazuka Miscellany.