There are two versions of Zotero. If you are a Firefox user and want to use Zotero within your browser, you can download Zotero for Firefox.
If you want to use Zotero with another browser, or if you want to use it with Firefox as a free-standing application, you'll need to download Zotero Standalone for your platform of choice (Windows or Mac). Make sure that you also download the appropriate browser extension for whichever browser you normally use (Chrome, Firefox, or Safari).
Both versions of Zotero and the browser extensions can be downloaded from Zotero.org.