Use jQuery's JSON call to the YouTube API to get the results back and then use jQuery to put the results where you want them. You can use firebug's NET tab to make sure you requests/respoonses are coming back correctly and then use console.log() to make sure you parsed the response correctly.
eg. URL:
GET https://gdata.youtube.com/feeds/api/videos/(the-video-id)?v=2&alt=json
More info: