Printing out a linked list using toString

public static void main(String[] args) {

    LinkedList list = new LinkedList();
    list.insertFront(1);
    list.insertFront(2);
    list.insertFront(3);
    System.out.println(list.toString());
}

String toString() {
            String result = "";
            LinkedListNode current = head;
            while(current.getNext() != null){
                result += current.getData();
                if(current.getNext() != null){
                     result += ", ";
                }
                current = current.getNext();
            }
            return "List: " + result;
}

As has been pointed out in some other answers and comments, what you are missing here is a call to the JVM System class to print out the string generated by your toString() method.

LinkedList myLinkedList = new LinkedList();
System.out.println(myLinkedList.toString());

This will get the job done, but I wouldn't recommend doing it that way. If we take a look at the javadocs for the Object class, we find this description for toString():

Returns a string representation of the object. In general, the toString method returns a string that "textually represents" this object. The result should be a concise but informative representation that is easy for a person to read. It is recommended that all subclasses override this method.

The emphasis added there is my own. You are creating a string that contains the entire state of the linked list, which somebody using your class is probably not expecting. I would recommend the following changes:

1. Add a toString() method to your LinkedListNode class.
2. Update the toString() method in your LinkedList class to be more concise.
3. Add a new method called printList() to your LinkedList class that does what you are currently expecting toString() to do.

In LinkedListNode:

public String toString(){
   return "LinkedListNode with data: " + getData();
}

In LinkedList:

public int size(){
    int currentSize = 0;
    LinkedListNode current = head;
    while(current != null){
        currentSize = currentSize + 1;
        current = current.getNext();
    }

    return currentSize;
}

public String toString(){
    return "LinkedList with " + size() + "elements.";
}

public void printList(){
    System.out.println("Contents of " + toString());

    LinkedListNode current = head;
    while(current != null){
        System.out.println(current.toString());
        current = current.getNext();
    }

}