To get the maximum benefit of using Zotero, make sure you download the word processor plugin in for Firefox. This will let you seamlessly add citations to your Word document as you are typing your paper.
Then click on the appropriate link (Windows, Mac or LibreOffice), and just as you downloaded Zotero, click "allow" to the pop-up, then "install" and then "restart".
To add articles to Zotero you just need to click on the paper icon in your browser. It will automatically be added to your Zotero Library:
NOTE: When adding articles, it is best to do it one at a time, rather than using an export feature in a database to save multiple articles at once. The reason is because the export feature generally only saves the citation, and the not the full-text of the article. When you add articles one at a time, you generally get the full pdf text along with the citation.
You can add a book directly from the catalog. Simply click on the blue book icon in your browser:
When you're ready to insert a citation in your paper, click on the Zotero tab and then "Add/Edit Citation"