You download Zotero from zotero.org. You need both the "desktop" piece (i.e. Zotero 6 for Windows, below) AND you need the Connector for your favourite browser.
If you are on a Mac, and/or using a different browser (Firefox or Safari), you will see options for downloading for Mac or for Firefox etc.
When you download the pieces mentioned above, a plugin for Word and/or Google Docs, will likely come with those pieces. If not, you can download the word or google doc plugin from the link lower on the Zotero download page - look for the Word Processor plugins on this page.
Please be aware that Lakehead has no institutional connection to Zotero, which is a freely developed and freely accessible online resource. Although the Zotero user forums are quite useful, Zotero does not provide official support to its users. Lakehead library staff will be happy to assist you with Zotero as a fellow user, but we will be unable to intervene on your behalf to address problems such as lost data, which was sometimes possible with RefWorks.