Depends on what distro you are running. If you are running a redhat based distro, if you configure your yum repositories you don't have to mess with tarballs too often. There are equivalent package managers for most distros.
Again with redhat based distros like Fedora, Mandriva, SUSE, etc you just need an RPM file to avoid having to mess with a tarball. I'd do a search on the package name and see if an rpm is out there. To use the RPM just download it and from the dir the rpm is in do
rpm -Uhv [rpmname]
There are GUIs that you can get from freshmeat.net which will make all of this a point and click exercise.
Now down to tarballs. Those are a last resort install for most Linux users. If you have to use a tarball because there is no rpm.
tar -xzvf name of tarball
tar -xzvf abcde.tar.gz
cd to the newly created dir
do an ls in the dir. Most will have a file called configure. If it does not read the included readme file. There is likely a binary install file you have to use. Flash for example will have you download a tarball to execute a binary install file.
./configure
make
make install
The make clean just restores the config file to how it was orgionally. You have to do ./configure again before using make typically.