There are many sites that provide sample letters for getting permission.  However one of the best is: http://landmark-project.com/permission1.php

Here is an email template that has worked for us.

Hello!

My name is _______________.  I'm a _____ grade student of the _______________ school in ____________.   I am working on _____________. We are creating a video that ___________________. We would really like to use the song ________________ in our video. Would you grant us permission to use this material for my class or help me contact the appropriate person(s) for gaining this permission?

Thank you!

Sincerely,

________________