As with other subcultures, science fiction fandom has its share of writers. Many of them publish amateur magazines for other fans to appreciate. The subject matter ranges from discussions of SF to humor to personal topics and everything in between.
In older times before photocopiers, fan publishers often printed their fanzines using spirit duplicators or mimeographs. Now we see a small but growing number of fanzines published on Web sites as HTML or Adobe PDF documents. Both paper and electronic formats have their good and bad points.
Most fan publishers accept cash payment of a few dollars for an issue of their fanzine, but would prefer that you write a letter of comment (LOC). Publication schedules can be erratic and depend on the publisher's whim and other commitments.
The best way to investigate this fascinating world is to check out fanzine reviews. Tom Feller publishes his reviews of recent fanzines in the SFC Bulletin, along with contact addresses for the publishers.
If you're interested in publishing a fanzine but don't want to print 100+ copies of your zine, check out the amateur press alliances or apa's. While the audience is smaller, an apa can provide more frequent and useful feedback.
Whether or not you get into fan publishing, you'll probably agree that science fiction fanzines are an island of idiosyncracy in an increasingly homogenized world.