Attach a click() event to the FaceBook 'Like' button?

Facebook API doesn't allows you to subscribe to the like clicking event, but it allows you to subscribe to the like happening event (fired when the like action is completed):

FB.Event.subscribe('edge.create', function(response) {
  // like clicked
});

see here.

One can detect 'like' and 'unlike' event of facebook like button using edge.create and edge.remove respectively.

Make a PHP (or whatever language you use) script to CURL the source from http://www.facebook.com/plugins/like.php?href=http%3A%2F%2Fwww.MySite.Com... blahblahblah

Put the source from facebook into your html page, you can then you can do whatever you like in JavaScript/jQuery with the code from Facebook.

Some examples for CURL within PHP - http://www.php.net/manual/en/curl.examples.php

You cannot use JavaScript to access elements within an iframe that does not belong to the current URL, as I guess the domain you're using is not facebook.com you won't be able to attach an event to the like button in this way.