After you install WinZIp, when you click the Help - About Winzip... button you will see a Register button.
Click on the Register button and you will get a dialog to enter the registration code - see the attachment.
After you have registered the product the Registration button turns into a License button - which simply brings up help on the license.
FWIW the install program (setup.exe) stopped with an error saying the timestamp of the README.TXT file did not match the timestamp of SETUP. I fixed that by running TOUCH *.* on the install files and restarting SETUP.EXE. Also the registration for later versions works on earlier versions, but not vis a versa - according to WinZip's website.