There are a few scenarios, here they are one at a time (as I feel like updating this). This assumes that the remote Linux box has a user account for you to login with, X applications and libs installed, a ssh server running, and no firewall, IP, or other network issues to contend with. The terms remote and local are relative to you.

Forwarding X from a Linux box to a Win32 machine

For this to work, you need a Win32 X server and a Win32 ssh client.

Install X-Win32, and start the X config utility from the start menu. On the window tab, set the screen resolution you want it to run at. I usually run 1 step below what I run my monitor at - so at 1280x1024, I run the X server at 1024x768. On the same tab, check the "single window" option to the left of the resolution. Go to the security tab, and enter the hostname or IP address of the RLB (remote linux box) as being a machine that it is OK to accept connections from. Go ahead and save everything, then shut down and restart the X server - you've used some of your 2 hour limit :)

OK, lets make a connection. Start up your ssh client, connect to the remote linux box, and login. Start up the X server on your local machine. Once you've authenticated in your ssh session, you need to export your DISPLAY variable so it is pointing back at the machine you are sitting at.

luser@remotelinuxbox:~$ export DISPLAY=ip.of.win32.box:0

Now all you need to do is start a X application. Personally, I just run startkde since I like the desktop, etc. but if you were just needing one app, then you could start it alone, like by running xchat. You probably do want some sort of window manager, so you may want to consider writing a "remotex" script that will load blackbox or something and then start whatever apps you like.