After adding an item to your library, click on the Attachments tab in the right-hand section of the Zotero pane. A pull-down menu will allow you to add a link to a file stored elsewhere on your hard disk, copy a file to your Zotero storage directory, add a link to the current web page, or save a snapshot of the current web page.

You can also drag the item from your computer's file system (hold down Shift [Mac] or Ctrl [Windows/Linux] while dragging to move, rather than copy the file) or right-click on the Zotero item and choose “Add Attachment”.