Here are some step by step instructions to help you get KDE running on Debian. It is assumed you have installed Debian but do not have an X interface yet.

Always update before installation
apt-get update
apt-get install x-window-system-core

You can install “kde” to get the entire KDE desktop system, or “kde-core” to install only essential KDE packages
apt-get install kde
###OR###
apt-get install kde-core

Install a display manager then test X
apt-get install kdm
startx

You should now have a graphical interface. If startx fails you will need to read the error messages and correct your xserver settings accordingly.
dpkg-reconfigure xserver-xfree86

After making your changes restart the xserver
startx