You can access the saved citations into your librayr in different ways, if you use the web version of Zotero please note there is a new feature called "Web Library" as shown below where you can access your different libraries. Zotero library consists of three columns:
If you prefer to use the older version of Zotero library, please go to your account menu and select "Use old Web Library"
The older interface of Zotero group will appear and you can switch between the two interfaces easily
If you use Zotero standalone you can move the items betweek libraries and groups by simply clicking and dragging them.
Note: If you select a collection, then close the Zotero pane, anything you add to Zotero will go directly into the selected collection.