You can not directly download videos from the new virsion of youtube.If you want to make search ,download and convert videos more easier and fun for you, ou can use
Video Download Studio to free search and download videos/audios from popular online social media websites like YouTube, Dailymotion, imeem, Break.com, Veoh, Yahoo video, Google video, MySpace, Vimeo, RuTube, Blip.tv, and many more!
It is really easy to use. Try iit and you will love it.