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When you installed Zotero, it included the word processor plugin for Microsoft Word and LibreOffice. In newer versions of Word, you'll see Zotero as a tab in the menu. In older versions, it's under the script menu.
Don't see Zotero when you open Microsoft Word? Open Zotero, go to Preferences, select Cite from the menu, select Word Processors, and click Install Microsoft Word Add-in.
This plugin works when your Zotero application is open. As you write, place the cursor where you want the citation. Click Add/Edit Citation, choose from your Zotero library, and watch it drop in your citation!
When you are done writing, select Add/Edit Bibliography. Zotero will take all your in-text citations (or footnotes) and create a bibliography.
Zotero works similarly in Google Docs. Your Zotero Connector added Zotero as a menu item in Google Docs. Add/Edit Citation will prompt you to search your Zotero library for the item you want to cite. When you are done writing, insert a bibliography with one click!