There isnt really much documentation out there to do this but I use this method and it works well for me.
To get started include the latest jquery library inside your <head> tags
<script src="//ajax.googleapis.com/ajax/libs/jquery/1.11.0/jquery.min.js"></script>
Next on the spot where you want to add in the video drop in the following code:
<div id="static_video"></div> <script type="text/javascript"> function showLatestVid(response) { if(response.data && response.data.items) { var items = response.data.items; if(items.length>0) { var item = items[0]; var videoid = "http://www.youtube.com/embed/"+item.id; console.log("Latest ID: '"+videoid+"'"); var video = "<iframe width='300' height='225' src='"+videoid+"' frameborder='0' allowfullscreen></iframe>"; jQuery('#static_video').html(video); } } } </script> <script type="text/javascript" src="https://gdata.youtube.com/feeds/api/users/*YOUR USERNAME*/uploads?max-results=1&orderby=published&v=2&alt=jsonc&callback= showLatestVid"></script>
Just change the *YOUR USERNAME* to your channel name.
That should do it.
UPDATE:
This method doesnt work anymore 🙁 , but here is the updated method: Embed latest video from channel