Protecting PHP scripts called via AJAX from evil

Hi folks,

I'm looking for a straightforward way to protect PHP files which are
called via AJAX from being called from outside my application.
Currently, someone could forseeably open the console and watch the
javascript post variables to a public file (actions/delete_thing.php)
and then use this knowledge to trash the place.  I found this thread
at stackoverflow which seems to cover the issue I'm looking at, but
it's pretty intense and I figure there's an easier way but I'm not
sure how.

http://stackoverflow.com/questions/2486327/jquery-post-and-php-prevent-the-ability-to-use-script-outside-of-main-website

It seems unlikely that this is the method everyone uses, but maybe
not.  Advice is nice.
Marc