Picking a random element from a set

How do I pick a random element from a set?
I’m particularly interested in picking a random element from a
HashSet or a LinkedHashSet, in Java.
Solutions for other languages are also welcome.

int size = myHashSet.size();
int item = new Random().nextInt(size); // In real life, the Random object should be rather more shared than this
int i = 0;
for(Object obj : myhashSet)
{
    if (i == item)
        return obj;
    i++;
}