I've been an admin on a couple of cichlid forums and a mod on others, but this is general and not to speak for management of this forum--
Unless you own or are partnered in a site, it's not typically something you volunteer for. I was asked in each instance. Generally it takes some years as part of a forum so that you're known, respected, and have a good reputation with members and staff. You need to be around long enough that management knows and trusts you. They have to be looking for someone. A fish forum typically wants someone with some knowledge of the fish. You need to prove over time that you're level headed, respectful to members, able to be diplomatic and good with people, willing to speak up when needed but not a hot-head, 'authority' doesn't go to your head, good judgement dealing with issues that come up, not a name caller or someone who frequently gets into spats with other members, sometimes you need to be able to handle some of the background software.
Edit-- I'd already written all this stuff, or I'd have left Hendre's post as already a good answer.