Once you've downloaded the necessary components, you'll need to extract the .ZIP file (or files if you downloaded the chunks). Be sure to use a 32-bit unzipper. The size and filenames in the archive are too much for a 16-bit unzipper. Examples of 32-bit unzippers include WinZip and PKZIP for Windows.
Both ZipSlack and BigSlack are designed to be extracted directly to the root directory of a drive (such as C: or D:). A \LINUX directory will be created that contains the actual Slackware installation. You'll also find the files necessary to booting the system in that directory as well.
After you've extracted the files, you should have a \LINUX directory on the drive of your choosing (we'll use C: from here on).