You don't, a tar.gz is an archive format like zip or 7z
Technically it's two formats a tarball - all files combined into one file, tar - and then compressed into a gzip.
To uncompress and release the files run:
tar -xzf filename.tar.gzMore info here: https://www.howtogeek.com/362203/what-is-a-tar.gz-file-and-how-do-i-open-it/
Its probably not a binary inside that archive... So you might need to extract and compile... But did you make sure a package was not available from AUR?
The AUR was bugged for me, So I went to their original site and downloaded it. What I ended up doing was to extract the folder to
/optand manually create thealiasand.desktopfile.
That's a archive. If it was advertised as something to install, then there might be something inside which can be installed, but there are different scenarios. It might be the source of a program, bundled with scripts to configure, compile and install it. It might be the compiled program with our without scripts to copy all the individual files to the right dirs. Maybe it contains just a script which fetches all the files online and installs them. It might contain a virtual enviroment and the program, it might contain another archive...