The Cygwin Documentation/FAQ says that to install X/Cygwin, just requires running the setup package http://www.cygwin.com/setup.exe and clicking on the install for X11.
The install system at first appears cumbersome, but is actually quite powerful once you understand how the View system works.
Installing X11, leaves you with an xterm shortcut in your start menu and on the desktop. Clicking on this icon, or any other programs in the X application list results in nothing happening!
You must start the X server first, which doesn’t seem to appear documented. To start the X server run C:\cygwin\usr\X11R6\bin\startxwin.bat . The X icon will be displayed in the system tray when the server is running. The best idea is to create a shortcut to this startup program.
You can now run xterm and any other application you want🙂