Visit zotero.org/download and select Zotero 4.0 for Windows or Zotero 4.0 for Mac depending on your operating system. Follow download instructions.
Next download the extension for Firefox, Chrome, or Safari by clicking on its icon under Zotero 4.0 for Windows orZotero 4.0 for Mac and following the instructions.
Zotero is best used as an add-on for Firefox. If you do not already have Firefox on your computer, go to mozilla.org and follow the instructions for the free download. If you prefer to use Chrome or Safari see the instructions below for Zotero Standalone.
While in Firefox, visit zotero.org/download and select Zotero for Firefox. When prompted click Allow, then Install Now, then Restart Now: