The Zotero toolbar can also be used in Google Docs, and makes, therefore, collaborative work easier. It is part of the Zotero Firefox and Chrome connectors (it does not work with Safari for the moment). A toolbar and a Zotero button are added in Google Docs and can be used to add citations and a bibliography, the same way as in Word or LibreOffice.
Zotero recommends to avoid having several people insert or edit citations at the same time. If you wish to start writing a document using Google Docs, then move it to Word or LibreOffice for final editing, you can do it while preserving active Zotero citations. Just select "switch word processors" in the Zotero menu in the Google Docs toolbar, save the converted file, and open it in Word or LibreOffice. The process should be reversible, but Zotero recommends performing the conversion in a copy of the file.