id="contactSuccess" style="display:none"

<script>
$("#contactForm").submit(function() {
    var url = "form.php";
    $.ajax({
           type: "POST",
           url: url,
           data: $("#contactForm").serialize(), // serializes the form's elements.
           success: function(data)
           {
               $$('#contactSuccess').show();
           }
         });
    return false; // avoid to execute the actual submit of the form.
});

</script>