Add this directly after the opening <body>
tag
<div id="fb-root"></div>
<script>(function(d, s, id) {
var js, fjs = d.getElementsByTagName(s)[0];
if (d.getElementById(id)) return;
js = d.createElement(s); js.id = id;
js.src = "//connect.facebook.net/en_US/all.js#xfbml=1&appId=477427382375494";
fjs.parentNode.insertBefore(js, fjs);
}(document, 'script', 'facebook-jssdk'));</script>
Then we add the like button somewhere below the facebook code we just added
<div class="fb-like" data-href="{facebook-page-url}" data-width="200" data-layout="button_count" data-action="like" data-show-faces="true" data-share="false"></div>
I assume you are using jQuery. So after jQuery is loaded, subscribe to the Facebook like and unlike events to have the information sent to Google Analytics.
<script>
(function($){
var track = function(action, url) {
// _gaq.push(['_trackSocial', 'facebook', action, url]); // old, legacy style analytics
ga('send', 'social', 'facebook', action, url); // new, universal analytics
};
$(window).load(function($){
FB.Event.subscribe( 'edge.create', function(url){
track('like', url);
});
FB.Event.subscribe( 'edge.remove', function(url){
track('unlike', url);
});
});
})(jQuery);
</script>