Below is a simple step-by-step guide on how to install Cygwin Perl on Microsoft Windows 7. The instructions should work on most versions of Windows from XP and up.
The instructions are supported by a series of screenshots. I've made all the (uncropped) screenshots available for easy reference/download.
Start Internet Explorer and open the Cygwin project website:

You might need to scroll down a bit to find the download link for the installation program, simply called
setup.exe
. Click the link:
A dialog will ask you if you want to run or save the file. Just click Run:

You'll get a warning about running a program from an untrusted source, click Yes:

The installation program will start, click Next:

The default location to install is C:\cygwin\, you should not need to change that, unless you have another disk and want to use that. Do not use directory names with spaces like c:\Program Files\. Click Next:

The installation program will download a lot of packages during the installation. The default directory is C:\Users\name\Desktop (where name is your username). I don't like clutter on my desktop, so I change that to C:\Users\name\Downloads. Click Next:

Unless you know you're behind a proxy, just click Next:

Select a download site and click Next:

You'll be presented with following window, where you can select which packages to install:

Just write perl in the search field and the list becomes a little shorter:

Click on the line that says "Perl () Default" to change it to "Perl () Install" and click Next:

The installer will resolve some dependencies that you'll need, just click Next to continue:

The installation will start:

You might get an error downloading packages:

Go back and select another download site:

I got some postinstall errors, but they were safe to ignore, i.e. just click Next:

By default you'll get some icons in both the start menu and on your desktop, untick any you don't want and click Finish:

The installation is complete, and you'll see new programs installed:

Select the Cygwin Terminal and a Terminal Window will open:

Do a perl --version to check the version of perl:

That's it. You've installed Cygwin Perl.