The Zotero web site (Zotero.org) has clear, simple documentation and video tutorials. Here is an introductory video.
Their Quick Start Guide provides an excellent overview. Here are some basic installation steps for Firefox, Chrome, and Safari:
To begin: Click the “Download Now” button
Download the Firefox extension
Also, be sure to click on “Add a plugin for Word or Libreoffice”
For Chrome or Safari
Download Zotero Standalone
Then add your browser extension (Firefox, Safari, Chrome)
If you are using a Mac, your screen will say “Zotero 4.0 for Macs”
Note: if Zotero does not appear to work correctly, you may need to close & re-open your browser at this point.
To set your Zotero preferences, open Zotero by clicking on the Zotero icon at the bottom of your browser (or Zotero standalone on your desktop).Then select the small gear icon and choose “Preferences.”