As you already know, Ubuntu doesn't update a major Firefox update to their repository. Here are the steps to do a major Firefox update on Ubuntu.
Launch Terminal on Ubuntu and type in the following:
Step 1 Add the Firefox Stable PPA to your system's software sources.
sudo add-apt-repository ppa:mozillateam/firefox-stable
Step 2 Update the source list.
sudo apt-get update
Step 3 Install the newest Firefox.
sudo apt-get install firefox
Then, just launch Firefox to see the updated version. Watch the whole process in the following video.