This HTML is fine:
<a href="#" id="contactUs">Contact Us</a>
<div id="dialog" title="Contact form">
<p>appear now</p>
</div>
You need to initialize the Dialog (not sure if you are doing this):
$(function() {
// this initializes the dialog (and uses some common options that I do)
$("#dialog").dialog({
autoOpen : false, modal : true, show : "blind", hide : "blind"
});
// next add the onclick handler
$("#contactUs").click(function() {
$("#dialog").dialog("open");
return false;
});
});