Firstly you have need to install a Cygwin package. Better way is taking the full version from Cygwin main site (cygwin.com). But it has a very big size. Alternative way has taken cygwin_trunc.tgz from ITK's ftp site or from the mirrors. It's truncated version, but this is quite enough for using Clip (even for building Clip from sources).
You must unpack cygwin_trunc.tgz in C:\ (root directory of disk C:), unpack cygwin_patch.tgz to the same place (this file contains some fixes for correct work), add c:\cygwin\bin in your PATH and add cygwin.reg in your system registry. After rebooting you can use Cygwin.
In addition you may install GTK+ packages (gtk_std_win32.rar and gtkextra_std_win32.rar) if you planing to work with GUI.
More information about working with Cygwin you can find in "Beginner's guide".