Knoppix is designed to be booted from a CD. I use Fedora Core (
http://fedora.redhat.com). It is very friendly and most things work by default.
Red Hat/Fedora is all about the newbies.
Ok about the installation process.....you've asked the question and the answer could probably be written as a book but here are two ways to install things.
RPM Package: If you download a file that ends in .rpm, you can install it using the following command "rpm -i whatever.rpm" from the directory that the file exists in.
From Source: If you download the source code to a program (it is an archive, usually ending in .tar.gz or .tar.bz2) then you must compile the program in order for it to run. Unzip and untar the archive (if you are unsure how then use google). Then you must compile, this is a process that varies greatly but usually it is done like this.
./configure
make
make install
Run these three commands from inside the first folder you got when you untarred the file. If this fails, see the README file from the folder.
The program you mentioned (firefox) does not install either way. It is a script, which means it does not need to be compiled. Simply download it (download the archive that DOES NOT have "installer" in the filename because that one is querky). Simply unzip and untar it into a folder and run "firefox.sh" and firefox will run.
Hope this helps