I just struggled through installing GMT under Cygwin, and since I not only had to rely on piecing together information from out-of-date online tutorials, but also on direct help from Kurt, I figured I would write everything down here for future reference and to also hopefully make someone else's life easier.
First things first, check your home directory:
Always check your home directory in cygwin to see if it is actually what it should be. When you install Fledermaus on your machine, it sets a 'HOME' variable that is Program File/IVS/Fledermaus. Now Cygwin thinks this is its home as well. The CCOM wiki offers this solution:
Once you are happy with your home directory, here are the steps I followed to successfully install GMT:
To test one of the examples GMT runs upon successful install, you can navigate to any one of the examples found in /GMT4.5.1/share/doc/gmt/examples/. Each ex directory will contain the example scripts, necessary files, and the resulting postscript. I found that to view these files, I need to make sure the X-windows environment is up and running (from cygwin command prompt, type startx). Then I use ghostview (gs) to view the ps:
here is the result: