If Zotero detects that you're looking at a book or article on a library catalog or database, or a site like Amazon.com or the New York Times, you'll see a book or page icon appear in the address bar of your browser. Just click the icon and Zotero will automatically save the source.
If you're on a page of search results with many items, you'll see a folder icon instead. Click this to get a list of all the items on the page, and check off the ones you want to save.
Zotero can't automatically capture citation info from some web pages, but you can still add them to your Zotero library.
Right-click in your browser and choose "Save to Zotero" from the menu. This will save a new "web page" item to your library. You can add information about the author, etc., if you wish.
This will also attach a snapshot of the page to the citation. Taking a snapshot saves a copy of the page to your computer. It includes the page's text and images, so if the page is removed later, or if you're offline, you'll still be able to view your copy.
Zotero automatically saves PDFs along with citations when possible (you can change this in the preferences menu if you wish.) Attachments take up space in your Zotero account -- you get 300 MB free and can buy more space if needed.
You can attach files manually by dragging a PDF (or other file) into your Zotero pane. Dropping a file onto a collection, or in between library items, will copy it into your library as a standalone item. Dropping it onto an existing item will attach it to that item. This is the easiest way to attach a copy of an article to its entry in your library.
Click the Zotero button at the bottom of your browser to open your library. At the top left is a folder button with a green plus sign. Click this to create a new "collection."
Create collections to organize your references. Collections are like file folders on your computer, but a reference can be in more than one collection at a time. In other words, a book on the Civil War could be filed in your "Civil War" collection, your "Georgia History" collection and your "19th Century America" collection without having to make three copies of the reference.
It looks a little different in different browsers.