See Using the Zotero Word Plugin for information about how to install the Zotero Word plugin. Doing this will add a Zotero tab to Microsoft Word.
The page also covers how to add citations to your Word document, how to create a reference list/ bibliography in various citation styles (APA, MLA, Chicago, etc.), and more.
See Using Zotero with Google Docs for information about how to add citations and create reference lists (in various citation styles) to documents created in Google Docs.
Note that you must use Google Docs in Chrome or Firefox; a version of the Zotero Connector for Safari that will work with Google Docs is not yet available.