Youtube has introduced Shorthened URL for its youtube videos. The short URL starts with youtu.be(keep dot before two characters in youtube) It is simple. Just copy the Youtube video id and place it after youtu.be/
If your youtube video link is http://www.youtube.com/watch?v=ldYWKTQTIFA
For this , the Video ID is ldYWKTQTIFA (The video ID is the 11 character after = )
So the Shorthened URL is youtu.be/ldYWKTQTIFA
P.S: Make a note that, www should not come before the short URL.
Alternatively Google has introduced shorth URL goo.gl for its service. It is not for customers use.