I use Debian wheezy and the official Firefox binaries.
Just go to the Firefox website and hit the download button. It'll give you a .tar.bz2 with
firefox/ inside. Extract that somewhere you have read/write access to--I used
/opt/firefox/. After that, add that directory to your
$PATH (e.g. open up
~/.profile and add something like
PATH="/opt/firefox:$PATH"). Firefox's own updater should be able to update the software with no problems. Setting up any sort of desktop or menu shortcut shouldn't be difficult, just set it to run
firefox (or the full pathname) and to use the icon in the
Admittedly, it's not the best solution, but it works and ensures you get timely updates straight from Mozilla, with all the dependencies included. However, you may run into troubles with update-alternatives and the like, and you might have to set some options in your desktop environment (if you use one). But in lieu of a proper Mozilla Debian repository (maybe there is one, I haven't checked), it's one of the easiest ways to go about it. Maybe someone a little more package-savvy than myself could write a script that automatically fetches the latest binary, packs it into a .deb, and adds the relevant metadata? I don't see why it would be too hard.