There is no manual on how to use the ajax in FA.
To make it simple please have a look in /sales/includes/ui/sales_order_ui.inc
Look up the function display_order_header, line 258.
First in the function the $Ajax is defined as global.
$Ajax->update($name) can be used either for a single Control (the Control name) or a span of code with div_start($name) and div_end(), where you can declare your own name and use it in $Ajax->update.
Everytime the $Ajax->update is called the specific Control/code is called.
By looking at the code here, I guess you will get a first hint of how to use it.
/Joe