YouTube has no real API method where you can retrieve your URL. Instead you have to follow YouTube´s simple convention, to put together the correct URLs for your video thumbnails. Let´s say, you want the thumbnail for following video:

http://www.youtube.com/watch?v=u1zgFlCw8Aw

Just copy the video id - in this case u1zgFlCw8Aw. The URLs for the thumbnails are simply built with this rule: http://img.youtube.com/vi/<VIDEO_ID>/<IMG_TYPE>.jpg

In our example, the available sizes are:

# Big image: 480x360
http://img.youtube.com/vi/u1zgFlCw8Aw/0.jpg

# Small thumbnail 1: 120x90
http://img.youtube.com/vi/u1zgFlCw8Aw/1.jpg

# Small thumbnail 2: 120x90
http://img.youtube.com/vi/u1zgFlCw8Aw/2.jpg

# Small thumbnail 3 (DEFAULT): 120x90
http://img.youtube.com/vi/u1zgFlCw8Aw/3.jpg

That´s it!