Hey, just a quick explanation.
You have the full, URL which is . You take the text after 'v=' and before '&', so it is 'UyWlBPTn4dA' that you wrap in the [YOUTUBE]UyWlBPTn4dA[/YOUTUBE], like that. :)
I have edited your original post for you, so it works.
If you have anymore questions, feel free to ask.