When working on a Windows machine in the UNM labs, you will want to connect to a linux machine so you can use a compiler (javac for Java, gcc for C, etc.). It is possible to just work in a terminal, but you'll have a much more pleasant time if you set up an X server so you can get the full GUI experience. In fact, this will become necessary if you are trying to remotely develop a GUI application.
If that all worked, you now can open up a text editor such as emacs in all its graphical glory.
Thanks to David Shubsda for pointing me to the instructions at http://fricke.co.uk/Teaching/CS251/