I was getting a bit annoyed at all the disjoint posts around the internet about making HTML5 work with my Firefox install on my work laptop so I thought I'd contribute to the noise.
Getting started, if you go to http://youtube.com/html5 and you see something like the screenshot below, you might want to try out my instructions.
You might see x264 also in red, this guide should fix that as well.
Install Debian multimedia repository
(As root) Add the repo to your sources:
echo"http://www.deb-multimedia.org jessie main non-free">> /etc/apt/sources.list.d/deb-multimedia.list
Update sources and install keyring and update sources again: