The official organization of non-profit club requires filing a few documents with federal and state governments. First, the organizing members of the non-profit club should form an LLC, which is a Limited Liability Company. You have other options, but an LLC is the simplest to form and provides all the necessary documentation to gain official non-profit status. You will then need to file for categorization as an official non-profit organization, which means that the club will be tax exempt. The most common tax-exempt status is the 501(c)3.
Once you have the official documents taken care of, you can open a bank account as a non-profit club and use the money held in the bank account to pay employees of the club. Not all non-profit clubs have paid staff, but if the organization grows large enough, it will need full-time workers who will need paychecks. Non-profit does not mean that there is no money involved in the operation of the club; it simply means that the club exists for a purpose other than to make a profit. Whatever money is left after expenses (such as overhead and salaries) are paid is returned to the organization to help it achieve its purpose or can be donated to other non-profit organizations.
Volunteers are the life blood of a non-profit club. Since a non-profit club is formed to achieve a purpose, it naturally draws people who are also interested in achieving that purpose, whether it be creating a community garden, helping drug-addicted youth, or educating people about the environment. Volunteers at a non-profit club may come on a one-time basis to help with big projects or events; more often, though, people who relate to the cause of the club want to help out regularly, as they get involved in the club activities and form relationships with other people involved in the club.
The surrounding community is a big part of a non-profit club achieving its purpose. Club members can talk to their neighbors and go to city government meetings to let their officials know what they're doing, how, and why. Sometimes the city government can provide support, if not monetarily then perhaps through helping with publicity or allowing the club to use government property for meetings. Letting the citizens of the community know about the non-profit club is very important. Individual donations of time, materials, and money may not seem like much one by one, but they add up to a sustaining force.