I need to send my contact form via ajax and then show pop-up message.
For example if I'll send form POST data to some url it should response with "OK" or "FAIL"
Drupal 6
A module is there for ajax submition
http://drupal.org/project/ajaxsubmit
$form['#ajaxsubmit'] = TRUE;
That will change your form behavior to ajax.
Drupal 7 core integrated it.
Use the JQuery Form plugin, it's very easy and practical to implement: http://jquery.malsup.com/form/#getting-started
you can use the ajax module(http://drupal.org/project/ajax) to ajaxify your form, to show the popup, use a module like bettermessages, or growl or something of the sort.
Joshua