Open terminal, type in su and then hit enter (it will ask for root password). If you don't know root pw, type in sudo passwd root and enter your username and password.
Then extract the .tar.gz with this command:
tar xvfz xampp-linux-1.8.1.tar.gz -C /xampp
Now everything is in the /xampp folder. To start it type in: /xampp/lampp/lampp/start