This may be the blind leading the blind, I am a Linux newbie myself, but I have been able to install tarballs no problem.
This is to be done in a shell window
tar -zxvf program.version.tar.gz
This will show you the processing of unzipping the tarball into a directory.
This will take you into the directory just made.
This runs a hidden file (hence the ./) in the directory which checks the system configuration and makes sure all the required libraries are there. If not you will be told what is missing, but that's it.
This starts the install process from what I have seen
su then prompted for your root password
This logs you in as root for the final step
This carries out the instructions in the install file of the current directory which basically installs the program.
From then just type the name of the program to run it.
Hope this helps and sorry if it's a bit sketchy, just sharing what I have learned as I stumble about.