tar -xvf will extract the compressed tar file.
tar -xvf mycompressed.tar.xz
In Linux a file can run from any directory.
Do you have root privileges on this system? Do you want only run to run these?
Do you want all users to run these? Do you want only yourself to run these?
Usually, if a file is for everyone to run... there are specific places Linux admins
put these. /usr/local is common. /usr/share is also common.
If you want only people with admin privileges, then /root is sometimes used.
/srv/bin is another common place.
You can run anything from anywhere, but just extract it where it make sense.
Sometimes you have to change ownership and executable permissions on files.