How do I use a PriorityQueue?

Use the constructor overload which takes a Comparator<? super E> comparator and pass in a comparator which compares in the appropriate way for your sort order. If you give an example of how you want to sort, we can provide some sample code to implement the comparator if you're not sure. (It's pretty straightforward though.)

As has been said elsewhere: offer and add are just different interface method implementations. In the JDK source I've got, add calls offer. Although add and offer have potentially different behaviour in general due to the ability for offer to indicate that the value can't be added due to size limitations, this difference is irrelevant in PriorityQueue which is unbounded.

Here's an example of a priority queue sorting by string length:

// Test.java
import java.util.Comparator;
import java.util.PriorityQueue;

public class Test {
    public static void main(String[] args) {
        Comparator<String> comparator = new StringLengthComparator();
        PriorityQueue<String> queue = new PriorityQueue<String>(10, comparator);
        queue.add("short");
        queue.add("very long indeed");
        queue.add("medium");
        while (queue.size() != 0) {
            System.out.println(queue.remove());
        }
    }
}

// StringLengthComparator.java
import java.util.Comparator;

public class StringLengthComparator implements Comparator<String> {
    @Override
    public int compare(String x, String y) {
        // Assume neither string is null. Real code should
        // probably be more robust
        // You could also just return x.length() - y.length(),
        // which would be more efficient.
        if (x.length() < y.length()) {
            return -1;
        }
        if (x.length() > y.length()) {
            return 1;
        }
        return 0;
    }
}

Here is the output:

short

medium

very long indeed

Just pass appropriate Comparator to the constructor:

PriorityQueue(int initialCapacity, Comparator<? super E> comparator)

The only difference between offer and add is the interface they belong to. offer belongs to Queue<E>, whereas add is originally seen in Collection<E> interface. Apart from that both methods do exactly the same thing - insert the specified element into priority queue.

from Queue API:

The offer method inserts an element if possible, otherwise returning false. This differs from the Collection.add method, which can fail to add an element only by throwing an unchecked exception. The offer method is designed for use when failure is a normal, rather than exceptional occurrence, for example, in fixed-capacity (or "bounded") queues.

Pass it a Comparator. Fill in your desired type in place of T

Using lambdas (Java 8+):

int initialCapacity = 10;
PriorityQueue<T> pq = new PriorityQueue<>(initialCapacity, (e1, e2) -> { return e1.compareTo(e2); });

Classic way, using anonymous class:

int initialCapacity = 10;
PriorityQueue<T> pq = new PriorityQueue<>(initialCapacity, new Comparator<T> () {

    @Override
    public int compare(T e1, T e2) {
        return e1.compareTo(e2);
    }

});

To sort in reverse order, simply swap e1, e2.

I was also wondering about print order. Consider this case, for example:

For a priority queue:

PriorityQueue<String> pq3 = new PriorityQueue<String>();

This code:

pq3.offer("a");
pq3.offer("A");

may print differently than:

String[] sa = {"a", "A"}; 
for(String s : sa)   
   pq3.offer(s);

I found the answer from a discussion on another forum, where a user said, "the offer()/add() methods only insert the element into the queue. If you want a predictable order you should use peek/poll which return the head of the queue."