In your database of choice, select the small bookmark button in the address bar which will allow you to add either the search results, or a specific book or article into your Zotero library. The icon will look different depending on what you are saving.
Once you have finished collecting citations in Zotero, select the ones you would like to export and right-click to select "Create Bibliography from Selected Items"
Select the citation style you are needing, and select how you'd like this exported:
If you selected "Copy to Clipboard"- open a document and paste your bibliography in!