I think there are two major ways to approach a new hackerspace, you can build it with your own money or talk to companies, try to get them excited about your idea and get some donations. Not like the other stories here, we had the second approach. If you choose or kind of happen to take the second one, it's important not to become attached to the companies and let them have any power over you.
About one and a half years ago, I started some promoting for my project to start a combined hackerspace for my and a neighbouring county. Both are very rural areas with the biggest city having about 50k people being in the middle of complete area, so my thought was, that more local spaces were not very efficient. I found a couple of people who were somewhat interested, but I made clear before we could start with an actual space, there would be a lot of work with bureaucracy, going from door to door at companies to ask for suppoort and other stuff, nobody wanted to do that, they only wanted a 'ready to use' space. After a few month when I basically was demotivated because of a lack of interest, I was approached by a small club in that said city, with about 15 active members, who had basically already done the work of the first year.
They started out as a couple of friends from school with the idea for a non profit and the goal to work on projects with people from different fields. When I joined, they were already established as a registered non profit and had some sponsors, but were still working in the homes of the members of the individual projects. The idea for a hackerspace just recently had come to them, or at least the work towards that had started recently. They already had convinced a sponsor to pay the rent, but when we found a good place to start, we couldn't get in touch with him anymore. So we had to dismiss that and look for other options.
We were allowed to use a room in a school, which is only partially in use, for our monthly meetings, so because a lot of the rooms are empty and a whole wing isn't used by students anymore, we approached the township if we could use one or two rooms for our hackerspace. Since that meant 24/7 access, power usage and some other 'problems', it wasn't easy to convince them. We were allowed to use 2 rooms, but we had to make some compromises, like we weren't allowed to use any machines or use anything that makes a mess, because it's a public building after all. The biggest problem is that we aren't allowed to change the basic infrastructure and don't have a workshop, but since most members are programming or working with electronics, it's a good place to start. We moved in and had our first real space!
That was about 10 months ago and with a growing number of members, equipment and ideas, we are reaching a point were the current space is becoming to small and are looking for a new solution.
Because of our outstanding PR people, we got a lot of expensive equipment donated as well as some really nice money donations. We decided not to spend the money on our own place but keep it for future infrastructure and member projects, because we think that is the better solution for all of us, since not every member is using the space.
We are currently ~50 members, have a place to work and are at a point where the local university campus comes to us if they run out of ideas for student projects. We do have a small annually fee of about 20 bucks, but that is only to cover the basic costs because we want to make technology and the equipment in the space available for everyone, regardless of personal circumstances. The local media has shown some interest in projects like the conversion of a small helicopter from a combustion to an electric engine, a life sized looping louie and the 'more regular' stuff like a self build octocopter and others. Other projects are for example our own management software or a brewing system.
We are not an 'older' hackerspace and have yet to learn a lot and expand our equipment, but I think it's still interesting for people who want to start something similar to see another approach. I've probably forgotten some parts, so if you have any questions, feel free to ask.