If your Linux skills are really zero, then you have 2 choices: (1) learn the skills you need and/or (2) get help, locally. It's not easy to walk people through an installation remotely - you need someone sitting next to you to lead the way.
There are installation instructions for Cygwin in the package documentation and at this wiki page. The reason why they are not more detailed is because to experienced users, this is a trivial exercise and does not require a tutorial. Unfortunately to beginners, it's probably gibberish. Still, this is how we all got started :)
You've installed Cygwin - good. Now you need the development environment. Run the setup again and when you get to package selection, look for the "Devel" section. You will need at least gcc, gcc-g++, make and fortran 77. Possibly more, depending on what DOCK 6 requires.
Now you need to learn how to:
- open a terminal
- navigate to wherever on disk you saved dock.6.3.tar.gz
- unpack a "tarball" using tar zxvf
- move into the newly-created dock6/install directory
- run the commands "./configure gnu", "make" and "make test"
- run the newly-created DOCK programs from the terminal
As others have suggested: you may as well just run Linux, as either a dual-boot or a virtual machine. A lot of people believe that Cygwin allows them to "do Linux stuff in Windows", but this is not really true. The skills required to use Cygwin effectively are, essentially, Linux skills, so you gain nothing in terms of Windows usage.
"The DOCK suite of programs requires on the order of 100 MB of disk space and 48 MB RAM." Does your Windows machine have that much memory?