I am running KDE 4.11.3 on Kubuntu 13.10. My laptop has a Radeon display card.

How do I install additional drivers in KDE?

I looked up System Settings and Software Sources. But there was no mention of 'Additional Drivers'.

How do I install proprietary drivers for the display card? (On a different computer running Gnome, in Software Sources, there is an additional tab for installing such drivers).

KDE doesn't provide tools to install graphics drivers. That's up to your distribution. It is possible that GNOME provides such a thing, or that the distribution you run GNOME on provides such a tool, I don't know.

Try looking in the package manager, I'm sure it has a package for the drivers.

Greetings!

Depending on your hardware the radeon driver fullfills most requirements. For a list of capabilities see http://www.x.org/wiki/RadeonFeature/.

If you really want to install the proprietary drivers, take a look at https://help.ubuntu.com/community/BinaryDriverHowto/AMD