The Zotero Add-on for Firefox is much more robust and different than the Chrome extension. Where the Chrome extension simply clips the citation information, PDF and/or snapshot of the webpage you want to cite, the Firefox Add-on offers a full on interface for organizing your clips.
To get started, make sure you Firefox browser is up to date. Once you are sure your browser is up to date, go to Zotero.org and click the red download button, or click here to be taken directly to the download page. You want to click the left download button from this page, the one that is for installing Zotero for Firefox.
Once the Add-on is installed, you will see it in the top right corner of your browser just to the right of the address bar.
To clip citation information, all you need to do is click the "page icon" next to the "Z" icon. You can also click the dropdown arrow just to the right of the page to select different clipping options such as with a snapshot or without a snapshot. As you can see in the screenshot below, we have clipped the same webpage twice; once without a snapshot and one with a snapshot.
A snapshot is a copy of the HTML code that makes up the webpage. This allows you to see the webpage exactly how it was when you first visited it, even if the page has been changed or deleted.
Zotero will also clip PDFs and images if that is what you are clipping.
As mentioned earlier, Firefox's Zotero is a bit more robust than Chrome's. One area this is true is that you do not need the Standalone version to use Zotero for Firefox, and even if you do have the standalone installed, you do not need to have it open. Zotero for Firefox provides an interface to manage your citations without the standalone version. All you need to do is click the "Z" in the browser toolbar at the top of the screen and the interface will open up. If you have standalone installed and opened, it will pull up the standalone version.