In most sources, Zotero automatically detects the type of resource you are looking, and the Zotero icon in Chrome changes to show that it has recognized something it can grab.
You don't need to download the PDF full-text from the database! Zotero will detect it, and add it from the database page.
To save the article, simply click the Zotero Chrome button icon.
If you are looking at a list of references, you may see a folder icon. This icon will prompt you to select multiple items from the list to save.
If Zotero does not automatically detect a resource: