Navigate to the Tor Browser download page.
Download the GNU/Linux .tar.xz file
(Recommended) Verify the file's signature.
When the download is complete, extract the archive with the command tar -xf [TB archive] or by using an archive manager.
You'll need to tell your GNU/Linux that you want the ability to execute shell scripts from the graphical interface.
Navigate to the newly extracted Tor Browser directory.
Right click on start-tor-browser.desktop, open Properties or Preferences and change the permission to allow executing file as program.
Double-click the icon to start up Tor Browser for the first time.
Alternatively, from inside the Tor Browser directory, you can also start from the command line by running:
./start-tor-browser