Most of AJAX code in the Drupal documentation focus on traditional json/_get() applications, which require json manipulation on information on arrival at client side.
But the real trick here is to get only the piece of HTML you need instead of rendering a whole page with header, footer and every element that renders with your content.
Here is where a not well documented argument on hook_menu comes in action.
The 'delivery callback' function manipulates the hook_menu output by default using drupal_delivery_html() which returns a full HTML render page.
What we need to do is define our own delivery callback function returning just the HTML information we want to render via AJAX on client side.
The code will look like this:
1. Define a link to execute the AJAX call:
<a class="btn" href="#" onclick="myModule_ajax_load()">Ajax Test</a>