Find the Full Text
If you use the browser extension to add a journal article reference, it will usually attach the full text automatically. However, if the PDF is not available in that particular database it may be available in another database.
To look for the full text elsewhere, right click the item in your library, then click on Find Full Text. The PDF will automatically attach to the item from another library database.
If Zotero can't find the full text, try requesting the article through Interlibrary Loan or you may be able to find a PDF in Google Scholar.
You can add a saved PDF by right clicking the reference and selecting Add Attachment > File.