Debugging KDE applications can be done on different levels. Most applications "talk" invisibly through debug statements while they are running. Looking at this information mostly gives you enough info to find out what went wrong. For further details, read the dedicated article about error messages.
On a different level we have post-mortem debugging. This is used after an application died, probably because of a programming error. The drkonqi dialog allows you to create a backtrace, and possibly find out where it went wrong.
There are debuggers like gdb which can do a lot more than just find out where it went wrong. You should read the man page of gdb to find out more, and possibly download 'kdbg', 'ddd', or 'inspire' which make gdb a lot simpler to use. Read Debugging with GDB for a detailed tutorial.