Click "Install CygWin Now" and a setup program will run on your PC.
The setup program will ask you several things (e.g., pick a mirror site).
When you run the setup, be careful when you reach the package selection screen. By default X is not installed.
When you see the list of packages, you need to scroll down to the very end and and locate the X package.
Click on the X-windows selection and change "default" to "install".
At the end of the installation, Cygwin will ask you to add an icon to the desktop. It's easier to have an icon to run Cygwin.
If the installation is unsuccessful, refer to Cygwin's website for trouble shooting (Sorry, I don't know enough of Cygwin to help with problem related to installation...)
In this window, you can type many UNIX commands (Cygwin is a package of UNIX tools for Windows). Type:
This will bring up a new window. You can minimize the Cygwin window and the startx window, but DO NOT exit either program !!!
Read the manual on how to use Putty:
Save the program in some directory and run it.
The relevant manua section is 3.4 (last I check):
Search for "forwarding" in this file.
To test if the setup works, type:
in the Putty window and a letter X should pop up in a window on your PC.