Hiding link from anonymous users
You don't so much configure the visibility of links directly, but rather you configure the permissions of specific content types, and any link to content of a particular type will either be visible or invisible depending on the permissions of the content the link points to.

You can configure the permissions on any given piece of content by going into the Permissions section in Administration and finding the content type you want to restrict permissions on, and configure those permissions (check boxes for view, create, edit, etc..) based on role appropriately.

If you need to configure access to specific nodes/content, then you might have a look at Content Access.