To connect to a domain choose Connect from the File menu. You can connect to the default domain using the credentials of the account in which you're running by leaving all the fields blank.
The Save this connection checkbox saves a shortcut for a connection so that when you run AD Explorer again it appears in at the root of the tree. Note that AD Explorer does not save your password when saving a connection so you must re-enter it every time you reconnect.
To delete a saved connection, select the connection in the tree and chose Remove from the File menu or the context menu.