Well, I know many people want to know how to do this and it's complicated to describe using words so I decided to make some screenies to tell people how to.
First of all find the video you want to put on your profile
Now find the link at the top of the page (Highlighted in blue)
What you want to do is copy everything after "http://www.youtube.com/watch?v=" (Including any underscores, dashes etc.)
You should have something like "_RSQKjpjj5s" copied, now you want to paste it in your Details which can be found by going to "UserCP" and then "Edit your Details" Now simply scroll down til you find "Youtube I" and paste it in the box
Now just save changes and it would of worked
If you want the video to automatically start then simply copy and paste this code:into the "Youtube Auto-play"Code:&autoplay=1