No need to log in as root(and not recommended), enter KDE as a user, open a terminal and type "su"(without quotes).
This will then prompt you for the root password.
after this you should get a "#" at the prompt indicating that anything run from this terminal will be run as root.
Now you can run the ATI installer by typing
(if you are within the folder containing the installer)
(if you are outside the folder)
remember to type "exit" once you are done to return back to a normal user
NOTE: if you error saying that "ati-driver-installer-X.XX.X-etc.run" is not excecutable, do this:
chmod +x ati-driver-installer-X.XX.X-etc.run
BTW...Welcome to LQ