A Zip file has nothing to do with Delphi (the programming system, anyway). In most cases, you can just run the Zip file at download and it will unzip its contents on your computer. In some cases, you need a program such as WinZip to unpack the file but most zip files can unpack themselves.
It looks like what you really want to do is copy a file from one place to another. In this case you want to copy it from a web location, I think. Look in Delphi Help for the CopyFrom procedure. That will copy a file from one place to another on a single computer. I'm not sure whether it will work when the source is on the web, but it might if you specify the web address in the source parameter. You might want to start a new thread to ask how to use Delphi to copy a file from a web application to your computer.
I have made some simple GetUrl() and GetHtm() functions for Delphi using Synapse as the backend (but simplified into functions for ease of use). These functions are available here if you need them: