A tar.gz is a compressed tarball, i.e. an archive. You can open and extract
them with Gnome's "file roller" archiver frontend the same way you would a
zip file.
As for how to install from one, depends on the tarball really. Most of the
time tarballs contain source code, which you will have to build yourself.
Usually you use make to build them, but some use different build systems.
Some tarballs might have a nice convenient script to do it all, or even
prebuilt binaries.
There should be a "readme" inside the tarball or on the project's site that
explains further.
