A .tar.gz file is a compressed file. As the user, decompress it, by typing
tar -zxvf <filename>.tar.gz
This un-tarring will create a new directory. Cd into this new directory and look for 2 files, called README and INSTALL. These files will tell you if there are any special ways to install your program.
Generally, it goes like this:
...type "su" (minus the quotes)
...type the root password
Easy as that!