A couple of quick WP-Ajax examples.

ajaxy.php

<?php

/*
Plugin Name: Ajax Demo
Plugin URI:
Description: Yes, this is an ajaxy plugin.
Author: Matsuzine
Version: 1.0
Author URI:
*/


add_action( 'plugins_loaded', 'up_initialize_plugin' );

function up_initialize_plugin() {
    new Admin_Ajaxy();
}

class Admin_Ajaxy {
    public function __construct() {
        add_action( 'wp_ajax_add_foobar', array( $this, 'receive_ajax' ));
        add_action( 'admin_footer', array($this, 'inject_javascript'));
    }

    public function receive_ajax() {
        // Don't forget to stop execution afterward.
        $whatever = intval( $_POST['whatever'] );
    	$whatever += 10;
        wp_send_json(array( 'whatever' => $whatever));

        wp_die();
    }

    function inject_javascript() {
        // Obviously hardcoded image id...
        $img = 4;
        $nonce = wp_create_nonce('image_editor-' . $img);
        ?>
        <script type="text/javascript" >
        jQuery(document).ready(function($) {
            var data = {
                'action': 'add_foobar',
                'whatever': 1234
            };

            // since 2.8 ajaxurl is always defined in the admin header and points to admin-ajax.php
            jQuery.post(ajaxurl, data, function(response) {
                console.log('Got this from the server: ',  response);
            });

            // an example of calling one of the core ajax methods...
            jQuery.post(ajaxurl, { 'action': 'image-editor', 'postid' : 4, '_wpnonce' : '<?php echo $nonce?>' }, function(response) {
                console.log(response);
            });
        });
        </script>
        <?php
    }
}