This JS requires jQuery. In fact, it’d be pretty useless without it. All you need to have some script tag thingies after bringing jQuery into the equation:
<script type="text/javascript" src="js/jquery.yt-api.js"></script>
index.html has a basic example but you should use the YouTube Data API as a reference since this is just a quick and dirty abstraction over that.
Although this currently relies on jQuery down to the core, I’m thinking of completely removing this dependency. It’d probably be more useful.