Getting a copy of WinZIP
You can download the latest version.
If you download the this version, you either have to pay for it, or
use an evaluation version.
For the evaluation version, use the button marked "Download Evaluation"
The University of Nebraska maintains a nice WinZIP tutorial.
The makers of WinZIP maintain a WinZIP FAQ.
Instead of using WinZIP, you can also use PKZIP. You seem to be able
to download PKZIP for free.