How do I start a site like this for a different subject?

THere are a few open source free PHP web applications that you can use. That use mysql database and PHP for them. Here is a list of the top 15 forum scripts that you download and use on any machine that has IIS (Internet Information System) on windows, Or Apache which is another free application that you can use on a windows, Linux or Mac OSX environment.

http://hellboundbloggers.com/2010/05/18/free-open-source-forums/

I've used a couple of them over here and they are not bad at all. Fairly easy to configure with some little modifications to the the files that need to be configured. Once confiured your up and running in no time.

This site is based on QSQA, It's an open source solution made specifically for Q&A Sites. It has its limitations (Mobile Support) but it's also open source and (to my knowledge) well documented.

They have a wiki for setup information and other random things here and you can download the source from their site here.

From the Lockergnome.net About Page:

Lockergnome.net is powered by QSQA, the open source question and answer platform. It utilizes features from Wikis, Blogs, Forums, and community controlled news aggregator and rolls it into one community-driven site that is always up-to-date and always changing with the latest and active questions.