The club I belong to (Windsor Modular Railroad Club) started out as a modular group that met twice a week in a church basement. The club owned the corner modules, staging yard, a filler module and the power supplies. Members brought their own modules. This lasted for a few years, but we quickly tired of setting modules up every other week to run for a few hours. We moved to a permanent location 6 or so years ago and are now building a permanent layout using club funds.
We started off by posting flyers at the local clubs and had couple gatherings at the public library to gauge interest and set things in motion. Having an open gathering like that is a great way to find out what people would expect from a club, what they'd be willing to pay, does someone know of a cheap place to meet, etc.
Our club runs with a small executive committee, President, Vice-president, secretary, treasurer and two directors. All positions, except President, are elected each year with the vice-president moving up to President to maintain some continuity between years. Our dues are currently set at $20/month (CND) and that covers our rent and expenses and slowly building our new layout. We have over 30 members, but with having expenses there is a threshold where dues have to increase if membership drops, but we have not had any problems with that and dues have been constant since we moved to our current location. We also do fund raising through pop/coffee sales and 50/50 draws as well as the occasional train show.
We have also just added an N scale layout to the original HO one to expand our appeal and attract more talent and members.
Good luck starting your club, it is a worth while endeavor.