What archive format you downloaded, *.bz2 or *tar.gz?
Usually it is "firefox-10.0.2.tar.bz2" so you do it this simple, get into a terminal and cd into the folder where your firefox*bz2 downloaded file is located then issue these three successive commands:
tar -xjv firefox-*.bz2
That should start firefox.
While you enjoy using linux you can read and consult a good tutorial download this
to your drive.
Hope that helps. Good luck.