I've just installed Arch Linux with KDE as a desktop environment. However after some initial steps I need to login as root so I hit
Ctrl-Alt-F2 and I was thrown into the terminal (black screen/white letters). How can I return back to my KDE desktop without rebooting?
You switched to a different "virtual console" – there are several separate 'workspaces' which you can switch between using Alt+Fnum (or, inside Xorg, Ctrl+Alt+Fnum), where num is the number of the virtual console. By default, text logins are available on the first six.
Depending on the method you started KDE, Xorg should be running on either VC #1 or #7.