Zotero 6.0 is a separate software download that is not tied to the browser. Standalone has connectors that work with Safari, Chrome, and Firefox.
You must have Zotero 6.0 open to use the browser connector icons. If you don't you will just be redirected to Zotero's website.
You do not have to install the word processor plugins with 6.0. The plugins are bundled with the software download.
To install the Zotero 6.0 software visit http://www.zotero.org/download/. You must have administrative privileges on your computer to download the software. Click on the link for the correct operating system and follow standard procedures for installing software on your computer. Zotero 6.0 comes with word processor plug ins, so you will not need to install these plugins.