To contribute your first article to Fanlore, you'll need to have a Fanlore account and be logged in with it. See Create An Account.
Another good starting point is to create a profile of your favorite fan writer or fan artist, using the fan profile template. Copy the template to your buffer. Enter the fan's name in the search engine, and, if there's no article about them already, you'll see the name in red, and a prompt to write an entry about them. Clicking the prompt takes you to the blank edit page. Paste the template into the edit page and start filling it in.
Help:People pages has some suggestions about what to include in the article.
Other users can edit the fan article you started, and you can edit existing fan articles. So if your favorite fan writer already has an article that you can improve on, the Edit selection at the top of the screen will let you do that.