If they are clicking a submit button it is technically already going to a new page.
Let say the form button is on order_brouchure.php. If the form tags action attribute is set to thank_you.php they will get sent to a new page.
<form action="thank_you.php method="post">
Now admittedly you may be using the same page to process the form as the form code it on and then you will just test to see if a $_POST value is set and if so display the thank you.
if (isset($_POST['name'])) {
echo "<b>Thank you</b>";
}
else {
// your form code here
}
If you need an actual popup window you would use javascript to open a new window when the new page is loaded.
window.onload=function() {
window.open('http://www.mysite.com/thank_you.php','mywindow','width=500,height=500,toolbar=0,location=0,directories=0,status=0,menubar=0,scrollbars=1');
}
Of course all those are some of the basic ways to do it, there are several other techniques that can be used that are quire a bit more involved.