How do I work with xx-tar-gz files?

This is the general practice on the Internet for compressing data or applications. The format of a file 'xxx.tar.gz' is the file name xxx (or application). The directory structure was tarred to condense the data within the directory. This is typically done to create tape archives. Then a program (gzip) was run on the tar file to compress the xxx.tar file leaving a xxx.tar.gz file.

Read the manual pages on "tar" and "gzip".

But the basic idea is

        gzip -dc foo.tar.gz | tar tvf -

        gzip -dc foo.tar.gz | tar xvf -