Java queues don't have enqueue and dequeue methods, these operations are done using the following methods:

Enqueuing:

• add(e): throws exception if it fails to insert the object
• offer(e): returns false if it fails to insert the object

Dequeuing:

• remove(): throws exception if the queue is empty
• poll(): returns null if the queue is empty

Take a look to the first object in the queue:

• element(): throws exception if the queue is empty
• peek(): returns null if the queue is empty

The add method, which Queue inherits from Collection, inserts an element unless it would violate the queue's capacity restrictions, in which case it throws IllegalStateException. The offer method, which is intended solely for use on bounded queues, differs from add only in that it indicates failure to insert an element by returning false.

(see: http://docs.oracle.com/javase/tutorial/collections/interfaces/queue.html)

You can also check this as this is more useful:

http://docs.oracle.com/cd/B10500_01/appdev.920/a96587/apexampl.htm

public String dequeue() {
    if (isEmpty()) {
        throw new RuntimeException("Queue underflow");
    } else if (first == last) {
        String f = first.item;
        first = null;
        last = null;
        return f;
    }

    String f = first.item;
    first = first.next;
    return f;

}
public void enqueue(String item) {
    Node x = new Node(item);
    if (first == null && last == null) {
        first = x;
        last = x;
        return; // return back when first node is enqueued
    }
    last.next = x;
    last = x;
}