You'll probably get flamed for posting a Java question, and redirected to a Java board somewhere else.
You need to remember your casts though. get(0) (as an aside, perhaps you should use getFirst() instead of get(0), it's probably faster) returns an Object, not a LinkedList.
Code:
process = new Process (arrive, service, pid);
// list.get(0).add(process); // Object has no add method
((LinkedList) list.getFirst()).add(process)
// finalChange = (Process)list.get(0).get(0); // same problem
finalChange = (Process) ((LinkedList) list.getFirst()).getFirst()
System.out.println (finalChange.pid);