Perhaps it could be the nature of your question. I don't feel there is a direct answer and so it can be a bit tricky to answer. I myself and hesitant to reply because I don't want to put out any false information or even sound discouraging.
If you are talking about setting up an 'open source' site in the sense that it is a wiki, like Wikipedia, then this isn't too complicated. There are actually several wiki platforms that you can install on your server and after some initial configuration and setting up the basic parts of your wiki, you can try to roll in users to populate the site with content, update things as necessary and such. Though I feel I should mention in this regard (being a wiki), Wikipedia has people to moderate content that is posted or updated in articles, as to prevent content that breaks their terms, or just false/incorrect information.
However, if you are talking about a completely open source website, in which the structure isn't that of a wiki, but something else. And the site itself, template, layout, colors, stylings as well as the content and structure all get developed and updated by an open source community... well I feel this is a much bigger undertaking. Personally I've never seen such a thing and it may be because such a site would be a huge challenge. Unless you've got your own personal server that you feel is uber secure, it can be risky to allow an entire site to be open source.
But then again, I am not even completely sure what your goal is for your open source site idea so perhaps sharing a few details might help give me direction and I could give you a better answer.