Zotero has two main methods of organizing your library: Collections and Tags
Zotero enables you to separate your sources into different collections or folders.
To add a collection, click the folder icon in the upper-left corner of your Zotero library.
This will create an empty folder. You can then drag and drop items from you "My Library" folder to your new folder, or you can save references directly to your folder by having it selected when you are saving into Zotero.
Along with basic info like title and author, Zotero will often save additional information, like the subject terms used in a database.
You can also add your own tags, and can even color code them for quick, visual organization!