All you will need to do is drag the button to your bookmarks (make sure to have your bookmarks showing (CTRL Shift B in Chrome).
When you start playing the YouTube video click on the quietube bookmark and you are distraction free.
Embedded below is a GIF followed by a 46 second YouTube tutorial. Thank you to my friend Layla Lyons for suggesting this video tutorial.
Click here for a blog post on 2 other sites that provide distraction free viewing from August of last year.