Stop MySQL: sudo /etc/init.d/mysql stop
Copy the existing data directory:  sudo cp -R -p /var/lib/mysql /path/to/new/datadir
Edit the MySQL configuration file: gksu gedit /etc/mysql/my.cnf
And the configuration for AppArmor: sudo gedit /etc/apparmor.d/usr.sbin.mysqld
Restart AppArmor: sudo /etc/init.d/apparmor reload
Restart MySQL: sudo /etc/init.d/mysql restart