You might want to read this: http://www.knoppix.net/forum/viewtopic.php?t=2638
For installing a program in Debian/Knoppix you mainly use apt:
su (to become root, or use a root shell)
dselect update (do this first so apt will know what's available)
apt-cache search firefox (test this) (don't have to be root for this)
apt-cache show mozilla-firefox (test this) (don't have to be root for this)
apt-cache policy mozilla-firefox (test this) (don't have to be root for this)
apt-get install mozilla-firefox -s (test this)
apt-get install mozilla-firefox (this would actually install firefox)
apt-get remove mozilla-firefox (to remove it)
apt-get --purge remove mozilla-firefox (to remove firefox and configuration files for it)

Once installed run update-menus as user to get it to the menu. If you can't find it look under the Debian menu item.