You need a small bit of jQuery, which means including the library in your head and having a small piece of script in the head aswell.
First add this to the head:
<script src="http://code.jquery.com/jquery-latest.min.js" type="text/javascript"></script>
That loads the latest version of jQuery for you.
Next you need to add the jQuery code in to make the nav work. Its a simple 3 line code that checks its been clicked and then toggles the display on and off.
<script type="text/javascript">
$(document).ready(function() {
$('#nav-icon').click(function() {
$('ul.menu').toggle();
});
});
</script>
As you can see, it finds the id nav-icon and when its been clicked, runs a function which toggles the visibility of the ul.menu.
jsFiddle Demo: http://jsfiddle.net/3w63B/2/
If you go on the mozilla developer network (link) or go to the jQuery API pages (link) you can pick up the basics pretty quick. It only starts getting difficult when you start getting jumping right into the deepend of what it can all do.
Hope this helps fella.