If all you want is to run the programs on the pi and have them displayed on your linux or windows box, then the links I sent you do exactly that. From a linux box you ssh -X and from windows instead you would use putty with X forwarding enabled. It's all in details on that link. This is by far the best approach since you have integration of native and raspberry pi apps in one desktop. Have you read the 2 articles?
If you are still insisting in a more traditional KVM like approach over IP, then you'll need to use something like tightvnc. The funny thing, most people end up doing VNC over an SSH tunnel, because VNC is insecure, and after a while, you get used to just starting the app you want instead of the whole desktop. Anyway, the VNC step by step is here http://elinux.org/RPi_VNC_Server
The condensed version if you've followed the instructions on the sidekick articles I posted earlier, you can then:
ssh -X raspberrypi
$ sudo apt-get tightvnc
$ tightvncserver :1
You will require a password to access your desktops.
Would you like to enter a view-only password (y/n)? n
New 'X' desktop is raspberrypi:1
Creating default startup script /home/fdion/.vnc/xstartup
Starting applications specified in /home/fdion/.vnc/xstartup
Log file is /home/fdion/.vnc/raspberrypi:1.log
And then from your desktop you use a vnc client (there's at least a dozen out there) and connect to raspberrypi:1 (because we started a listener on 1).
I could also have started tightvnc with a resolution, to force a specific desktop size, ie:
$ tightvncserver -geometry 1024x768 :1
If you reboot, the vnc server will not restart automatically, but the elinux tutorial has that covered too.