To use an external script with ajax, you must register an action to trigger it. To do it, you need to use wp_ajax_YourAction and wp_ajax_nopriv_YourAction
add_action('wp_ajax_YourAction', 'myAjaxFunction');
// just a way to quickly print your js
add_action('wp_head', 'print_js');
function print_js(){
?><script type="text/javascript" >
jQuery(document).ready(function($) {
var data = {
action: 'YourAction',
fun: '42',
};
$.post(ajaxurl, data, function(response) {
console.log(response);
var json = $.parseJSON(response);
alert('the fun number is'+response.fun);
});
});
</script><?php
}
function myAjaxFunction(){
if(isset($_POST['fun'])){
$action = $_POST['fun'];
}
switch ($action) {
case 'fun':
echo json_encode(array('fun'=>$_POST['fun']+1))
exit();
break;
default:
break;
}
Depending on how your want to trigger your ajax call and the datas you want to post, this is just a simple example.