First, download the appropriate tarball for your system. The 32-bit builds are easy enough to find (see links above), but if you want to get a 64-bit build they can be found at http://ftp.mozilla.org/pub/mozilla.org/firefox/releases/latest/linux-x86_64/en-US/ and http://ftp.mozilla.org/pub/mozilla.org/thunderbird/releases/latest/linux-x86_64/en-US/ (note the locale at the end). Simply place the unpacked directories in /usr/local/bin.
The easiest way to keep Firefox and Thunderbird up-to-date is to use the built-in automatic update feature. In order for this to work, Firefox and Thunderbird need to be owned by a user who will actually run them on a regular basis. In my case, they are owned by my user account. Other users who have an account on my machine can use them, but all of the updates get installed by my user. You can just chown -R user /usr/local/bin/firefox, etc.
Now we just need to get them put into the applications menus. For this, we just need to put .desktop files in /usr/local/share/applications.
firefox.desktop should look something like:
Comment=Browse the World Wide Web
thunderbird.desktop should look something like:
Comment=Read/Write Mail/News with Thunderbird
For KDE 4, you may need to run kbuildsycoca4 to update the menus. Now you should see the official builds of Firefox and Thunderbird in the applications menus.
Firefox icon on Gnome 3 menu on Debian Wheezy
Firefox and Thunderbird icons on KDE 4 menu on Debian Wheezy
Update: I now have a video on Youtube demonstrating these steps.