Ok, let's see... and let me do some questions. Have you any experience on the command line, e.g. do you know basic commands like cd, ls, pwd...? Indeed the tutorial I linked explains how to do things from command line, so you have to open a terminal and type exactly what the instructions say (but always try to verify what you are going to do, since suggested command from anyone in the world must be trusted without knowing if they can mess your system up).
I suppose you have downloaded the last version on your desktop, so you will have something like
alex@linux:~> ls -l ~/Desktop/thunderbird-220.127.116.11.tar.gz
-rw-r--r-- 1 alex users 11442355 2007-10-06 10:06 Desktop/thunderbird-18.104.22.168.tar.gz
Ok, the first thing is to unpack the tar.gz archive and extract files in /opt. To do this you have to be root, but since in Ubuntu you can't login as root, the way is preceeding any command by sudo
sudo tar -C /opt -zxvf ~/Desktop/thunderbird-22.214.171.124.tar.gz
See the manual page for tar to learn about options: in brief this uncompress (-z) and extract (-x) the archive (-f) specified and put files in directory (-C) /opt. Doing this it tells you what's going on (-v).
The archive already contains the thunderbird executable, so you have to link them somewhere under your PATH. A good place can be /usr/local/bin:
sudo ln -s /opt/thunderbird/thunderbird /usr/local/bin/thunderbird
Finally if you want to have a desktop icon, you should create a file .desktop (a sort of descriptor) under /usr/share/applications. Again by root permission, you will open a text editor to create the new file
sudo gedit /usr/share/applications/thunderbird.desktop
Paste and copy the suggested text, save and all should be done. Advices from jschiwal and pixellany are wise: installing from a software manager let you have a software specifically built for your linux distro and can spare you some headache. Furthermore it can be more easily managed (verified, updated, unistalled and so on...). By the way, it is known that under the Ubuntu repositories there is an old version of Thunderbird, so if you want the very latest version this is the right way to proceed. I also suggest to carefully read the Ubuntu Documentation here