You must install enough Cygwin packages to support building GHC. This means selecting at least the following packages in the installation dialogue:
To see these packages, click on the "View" button in the "Select Packages" stage of Cygwin's installation dialogue, until the view says "Full". Note: Don't use the cygwin git (you'll get various failures, e.g. fork failures, with Windows Vista or Windows 7). Use http://code.google.com/p/msysgit/ instead.
Now set the following user environment variables:
Add c:/cygwin/bin and c:/cygwin/usr/bin to your PATH
Set MAKE_MODE to UNIX. If you don't do this you get very weird messages when you type make, such as:
/c: /c: No such file or directory
Set SHELL to c:/cygwin/bin/bash. When you invoke a shell in Emacs, this SHELL is what you get.
Set HOME to point to your home directory. This is where, for example, bash will look for your .bashrc file. Ditto emacs looking for .emacsrc
Here are some things to be aware of when using Cygwin:
Cygwin implements a symbolic link as a text file with some magical text in it. So other programs that don't use Cygwin's I/O libraries won't recognise such files as symlinks. In particular, programs compiled by GHC are meant to be runnable without having Cygwin, so they don't use the Cygwin library, so they don't recognise symlinks.
Some script files used in the make system start with "#!/bin/perl", (and similarly for sh). Notice the hardwired path! So you need to ensure that your /bin directory has at least sh, perl, and cat in it. All these come in Cygwin's bin directory, which you probably have installed as c:/cygwin/bin. By default Cygwin mounts "/" as c:/cygwin, so if you just take the defaults it'll all work ok. (You can discover where your Cygwin root directory / is by typing mount.) Provided /bin points to the Cygwin bin directory, there's no need to copy anything. If not, copy these binaries from the cygwin/bin directory (after fixing the sh.exe stuff mentioned in the previous bullet).