Zotero can be used with Google Docs in the same way as with plain-text documents or emails. See the screencast on Zotero and Google tools.

• To add a bibliography, simply select items in Zotero and drag them into the document.
• To add a citation, hold the Shift key before dragging.

To use a different style, change your Quick Copy settings in the Export pane of the Zotero preferences.

At the moment there is no way to get an automatically updating bibliography in a Google Docs document. (There are several requests to the Google Docs team for allowing Zotero integration.)

One possible workaround is to write citations such as ”{Smith, 2000}”, export from Google Docs to Rich Text Format (RTF), and use Zotero's RTF Scan feature. You'll have to do this each time you want to see your bibliography, though.