Go to the Zotero Downloads page. It should detect your operating system and browser, and present you with the proper version of Zotero to download, as well as the Connector for the browser you are currently in. Simply click the the appropriate buttons to download the standalone application and browser Connector.
Also browse Zotero plugins for additional tools, including plugins for Microsoft Word and LibreOffice.
Using Zotero on a GC computer? Consult our guide to adding the Zotero Connector to your browser on GC computers.