1) Post your video on Facebook.

2) Go to MyVideos and put your mouse cursor over the video title. Copy the URL. In Firefox, right-click your mouse and select "Copy Link Location"

Your video URL looks something like this:

http://www.facebook.com/video/video.php?v=123456789012345

3) Remove /video/video.php? and replace it with /v/ so the URL now looks like this.

http://www.facebook.com/v/123456789012345

Warning: Use such links for friends and family only. I suspect that Facebook would not be happy with you if you chose to put the link on a high traffic website or forum.