Zotero calls its folder structure "collections." Collections allow for hierarchical organization of references, but references can also be in more than one collection simultaneously (without duplication).
New Collection...button in the Zotero navigation pane.
New Subcollection...to add subcollections.
Items are automatically added to whatever collection is selected in Zotero when a citation is imported from the Zotero Connector, so make sure to select the collection you want before you begin saving citations. Citations can be dragged and dropped into different collections within Zotero after they have been added.
References in Zotero can be tagged with keywords. To add tags to an item:
Tagstab in the right pane
Once your references are tagged with keywords, you can use the tag selector to view all items with a given tag or set of tags. Tags can also be color coded, which places a colored icon next to the item's title in the central pane.
Notes allow you to add notes or comments to item records in your Zotero library. To attach a note to a record:
Notestab in the right pane
Addand add your note
Zotero also allows standalone notes, which are not attached to a specific item record but will appear in Zotero's central pane. To create a standalone note:
New Notebutton in the Zotero menu bar
New Standalone Note
For more help organizing references, see Zotero's very thorough documentation.