a tgz extension is just a shorter way of saying tar.gz
its a gzipped tar archive. (yeah, aload of files compressed into one)
you can decompress it with the command line
tar -zxf the_file.tgz
now you can access the files within the archive, and do whatever you want with it.
without saying what shorten.linux.tgz is, nor what files are in the archive, i dont know what u want to do with the compressed files...
maybe its source code u want to compile ?
if so, it should come with README / INSTALL files.. but the usual way is
make install (or /usr/local/sbin/checkinstall ) depending on if u have checkinstall installed.