Neeraj outlined the basic idea, but here are a couple of details you might keep in mind.
1) Java's garbage collection features make removing a Node from a linked list easier, as you don't have to explicitly set a pointer to a Node to null.
2) When implementing a remove(Object key) method for your own linked list, you'll start to appreciate why Java included Iterator interfaces. You might want to implement your own iterator() function in your linked list that returns a special implementation of Iterator to remove Nodes in your linked list. That will make your code more readable and more OO.