Just put a div on the page and use jQuery's append()
to place your data in it like so...
<div id='post-result'></div>
<script>
$(document).ready(function(){
$("button").click(function(){
$.post("result.php",
$('#searchForm').serialize(),
function(data,status){
//alert("Data: " + data + "\nStatus: " + status);
$('#post-result').append(data);
}
);
});
});
</script>
UPDATE - as per comments, added call to serialize the form so that the script will post the current form data to the server on submit.