A plain `.tar` archive created with `cf` (with or without `v`) is uncompressed; to get a `.tar.gz` or `.tgz` archive, compress it:

 gzip < my_files.tar > my_files.tgz

You might want to add `-9` for better compression:

 gzip -9 < my_files.tar > my_files.tgz

Both variants will leave both archives around; you can use

 gzip -9 my_files.tar

instead, which will produce `my_files.tar.gz` and delete `my_files.tar` (if everything goes well). You can then rename `my_files.tar.gz` to `my_files.tgz` if you wish.