Using Zotero in Google Docs is very similar to using it in Microsoft Word. When you download the Zotero Connector for Chrome or Firefox, you'll be able to use Zotero with Google Docs. Note: The first time you use Zotero with Google Docs you will have to link it to your Google Drive account. It may ask you to repeat this step every time you start using Zotero with a new document.
You'll find a Zotero tab along the top of your document, between "Add-ons" and "Help." This tab has all of the same options that the Zotero tab has in Microsoft Word: Add/edit citation, Add/edit bibliography, Document Preferences, Refresh, and Unlink citations.
One thing to note about Zotero and Google Docs is that while it works the same as with Microsoft Word, it tends to take a bit longer to do each of these steps.