It's easy to create a bibliography from your Zotero library.
Select the references or collections you want to include. Hold the control key (or command key on a Mac) and click to select multiple items. Right-click one of the selected items and choose Create Bibliography.
Choose the bibliographic style you want, select Copy to Clipboard, click OK and paste into your word processor.
Visit Zotero's Style Repository to save and use any citation style you need for your bibliography. Click on your desired style and save it to your computer.
The style will be uploaded to Zotero and available for you to use.
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. Search for the reference you want to cite and press Enter. 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 Doc Prefs").