<scriptlanguage="JavaScript">
$(document).ready(function(){
$('#YOUR_FORM').submit(function(){// catch the form's submit event
$.ajax({// create an AJAX call...
data: $(this).serialize(),// get the form data
type: $(this).attr('method'),// GET or POST
url: $(this).attr('action'),// the file to call
success:function(response){// on success..
$('#DIV_CONTAINING_FORM).html(response);// update the DIV}});returnfalse;});});</script>
EDIT
As pointed out in the comments sometimes the above won't work. So try the following:
<scripttype="text/javascript">var frm = $('#FORM-ID');
frm.submit(function(){
$.ajax({
type: frm.attr('method'),
url: frm.attr('action'),
data: frm.serialize(),
success:function(data){
$("#SOME-DIV").html(data);},
error:function(data){
$("#MESSAGE-DIV").html("Something went wrong!");}});returnfalse;});</script>