Apparently people are having difficulty updating to Firefox 3.6 on Ubuntu for all users, since it's not yet in the official Ubuntu repositories.

Here's an easy way to do it with a few commands, although I can't guarantee this will be compatible with future repository based updates. But it won't break anything.

1.) Download the Linux tarball file from Mozilla.

2.) Lets assume you saved it to your home directory. Unpack the tarball with Archive Manager, or on the command line as follows:
bunzip firefox-3.6.tar.bz2

3.) Open up a command prompt, which will normally start you in your home directory by default. Use this command to copy the files to the appropriate system folder (you'll be prompted for your password):
sudo mv firefox/ /usr/lib/firefox-3.6

4.) Replace your current execution command link with a link to the new binary with these commands:
sudo rm /usr/bin/firefox
sudo ln -s /usr/lib/firefox-3.6/firefox firefox

5.) (Re-) Start firefox and be greeted by the 3.6 welcome page. You're done!

If for some reason you want to downgrade back, remove the link we just created:
sudo rm /usr/bin/firefox

Then look for your original version with this command:
ls -d /usr/bin/firefox*

You should see something like firefox-3.0.17. Make a note of it, and replace my example in this command:
sudo ln -s /usr/bin/firefox-3.0.17 /usr/bin/firefox