You take the random characters from the end of the video's URL and place them in the [youtube][/youtube] tags.
For example, for the video "http://www.youtube.com/watch?v=lzjl0Cu9HgM" you would take "lzjl0Cu9HgM" from the end and put it between the youtube tags.
It would become this. [youtube]lzjl0Cu9HgM[/youtube]
Which would show as this.