Some databases do not work with Zotero's auto-detection feature (that is, there is no Zotero translator for those databases). Saving items from these databases requires extra steps.
Save the items in the database, then look for an option to export them. Export them in an RIS format. They may automatically save into Zotero, or you may have to use the Zotero menu and choose "import".
Zotero and MOST Databases
For MOST databases, Zotero works via the automatic detection feature -- that is, when you have a page of results, a folder icon shows up in the upper right side of your browser. When you click on the folder, you get a box listing all of the items from the page of results, and you check the items you want to save into Zotero, then click "OK" and they will be saved into your library:
When you are displaying a results page with a single item (a book, an article, a movie, etc.) the Zotero icon changes to reflect whatever type of item is displayed, as in the article example below. Click on the icon to save the reference: