You can also take a look at this guide published by the Zotero developers themselves.
Zotero will run on any operating system. Installation only takes a few seconds.
Open http://www.zotero.org/ and click the red "Download Now" button. You have a choice to download the current version for Firefox, OR choose the standalone and a browser connector for that.
Problems installing? Check the Zotero installation page.
You can view a number of video tutorials through the Zotero site.