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, select Copy to Clipboard, click OK and paste into your word processor. This method works with any word processor (or anywhere you can paste text).
Zotero offers word processing plugins for Word and LibreOffice. The plugin adds a Zotero toolbar to your word processor that allows you to add citations to your document while you write, and it automatically installs with Zotero if you have Word or LibreOffice on your computer.
To add a citation, click the first button ("Add/Edit 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 "Insert Bibliography" button. Your bibliography will appear, and new citations will be added automatically. Change bibliographic styles with the "Document Preferences" button.
The toolbar looks different on different operating systems and versions of Word. Mousing over the toolbar will pop up each button's function if they're not clearly labeled.
Zotero comes with the most common bibliographic styles, but many more are available to download.
To install a style from the web: