Because of a situation with the Debian Iceweasel maintainers’ packages for the current release (18) on Testing (wheezy), I decided I could as well take this opportunity to try to install upstream Firefox in the cleanest fashion possible.
I have actually run upstream Firefox on Debian GNU/Linux (even Nightly, or Minefield back when it was called that) in the past on multiple occasions, facing various awkward desktop integration issues along the way. Additionally, the Firefox binaries had to reside deep within my home directory, which seemed a little tacky. But I just found out that this does not necessarily have to be the case.
While searching for information about installing the original-brand Firefox on Debian, I came across this forum topic and quickly worked out my way from the instructions presented there. I think I’m missing the OP’s context for the switch (Iceweasel 3.5 on squeeze maybe?), but that is not terribly important now, three years after the fact.
There are alternative guides floating around which advise adding foreign distribution repositories to your APT sources. Needless to say, this is a really bad idea unless you are very sure of what you are doing. (Hint: You are not.)
Many of the following instructions are pretty much the same as in the forum post, just adapted to account for some minor changes over time, as well as some personal preferences. I also find my version of this guide much more palatable in presentational terms. Additionally, I am particularly adamant about not changing anything in /usr for this procedure, preferring /usr/local instead in order to avoid package conflicts in the future.