You can generate a bibliography in two major ways with Zotero.
A quick way to insert a bibliography into a paper (or any e-mail or other window where you can write) is to right-click on a collection (a folder) in the left Zotero pane and select "Create Bibliography From Collection..."
You will be able to choose any available citation style (if you want more options, use the Styles tab in your Zotero preferences), and whether you would like the bibliography as a text file (RTF), viewable in the browser (HTML), copied to the clipboard (where you can subsequently paste it into any open application), or as a printout.
A more robust way to generate a bibliography is to install the MS Word plugin so that you can insert citations and a bibliography into your paper as you write.
See more information on the Zotero website or watch the demo video below (links to video window; no sound):