Zotero offers word processing plugins for Microsoft Word and LibreOffice/OpenOffice/NeoOffice. The Zotero plug-in for Word should download automatically when you install Zotero on your computer. If you need to reinstall, follow the directions here.
The guides below show how to use Zotero to create in-text citations and bibliographies with Google Docs.
Using Zotero with Google Docs (Northwestern): Shows how to drag and drop citations from Zotero to Google Docs
Google Docs and Zotero (Princeton): Includes a keyboard shortcut as an alternative to the drag-and-drop method