Folders in Zotero are called collections. You can put an item in multiple collections without duplicating it. All items are always accessible from the main library.
Click the tan folder icon above the library panel to create a new collection.
Right click a collection to create a subcollection.
Drag and drop to add items to collections.
You can also add items directly to collections when you use the browser connector to add items to your library.
By default, items in subcollections do not appear in the top level collection folder. To make items in subcollections visible, go to View > Show Items in Subcollections.