Once you have Zotero and the connector installed, you can start importing references to your library. The Zotero application must be open in order to save references from your browser.
The Zotero icon in your browser (found in the top right with your other extensions) changes depending on the type of content you are looking at. Simply click the icon once to save an item to your library.

If you're on a page of search results with many items, you'll see a folder icon. Click this to get a list of all the items on the page, and check off the ones you want to save.
