When you open Google Docs in a browser that has a Zotero connector installed, you will see a Zotero option added to your menu.
Interacting with the Zotero functionality for the first time in a document will prompt you to authenticate the plugin with your Google account. Once authenticated you can begin inserting citations from your Zotero libraries.
To add a citation to your document, you can choose "Add/edit citation" from the menu or click on the Z button in the Google Docs toolbar. You will be prompted to choose your citation style.
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Installation
Where is the Zotero menu in Word?