generally speaking, ( this is not always the case ), tar files are source archives. To install them, you have to extract them (we'll get to this in a minute) and build them with your system's compiler. To extract a tar file, you need to know how it was compressed. You can tell this by what extension the file has. The two most common methods is gzip (which will end in tar.gz) and bzip2 (which will end in tar.bz2).
for a gzip compressed archive:
tar -zxvf tarfile.tar.gz
will extract the contents
for a bzip2 compressed file:
tar -xvfjp tarfile.tar.bz2
will extract the contents.
The actual steps involved in building vary from package to package but in the most basic form ( I stress basic here):
But keep in mind you kinda need to know what your doing if your upgrading libraries or the application needs to link against libraries installed on your system ( This is distribution specific, some require more steps than others).
if you use gnome/kde, then file-roller/ark will uncompress the archives for you also.