You use LinkedList if you want to store a list of objects, and if LinkedList is preferable to other List implementations (such as ArrayList) in the context of your particular requirements. You will find that sort of thing covered in the Collections tutorial:
http://java.sun.com/docs/books/tutorial/collections/
You don't use LinkedList or List. List is an interface that is not instantiable, LinkedList is a concrete implementation of that interface. You use a List, regardless of implementation, when you need the functionality of a [url=http://java.sun.com/j2se/1.5.0/docs/api/java/util/List.html]List[/url].
As to whether or not using a LinkedList or ArrayList or some other implementation is most appropriate for your requirements, see the Collections information that was linked to earlier.
Also note that in general a good programming practice is to define by an interface. Thus it will not be uncommon, and is almost always preferable, to see type defined as a List rather than a specific implementation of List.