Zotero offers word processing plugins for Word and OpenOffice. The plugin adds a Zotero toolbar to your word processor that allows you to add citations to your document while you write.
To add a citation, click the first button ("Insert Citation") on the toolbar. Select the reference you want to cite and click OK. Zotero will add the citation at your cursor.
At the end of your paper, click the third button ("Insert Bibliography"). Your bibliography will appear, and new citations will be added automatically. Change bibliographic styles with the last button on the toolbar ("Set Document Prefs").
It's easy to create a bibliography from your Zotero library.
Select the references or collections you want to include. Hold the control key and click to select multiple items. Right-click one of the selected items and choose Create Bibliography. Choose the bibliographic style you want, and select the output format: Save as RTF or HTML, copy to clipboard or print. (The RTF file format is compatible with all word processors.)
Or you can just drag and drop references from Zotero into your document! They'll turn into fully formatted citations. This works with any word processor including Google Documents. To insert an in-text 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.)