Zipping files is easy on the Mac. You just right-click on one or more selected files in the Finder, then click Create Archive. The files get turned into an easy-to-handle .zip file.
On iOS, it’s a bit trickier. Even in iOS 11’s new Files app, you’ll find no built-in support for zipping files into a single package (or for unzipping them). To zip files in iOS, I use Readdle’s excellent Documents app. Lots of one-shot iOS apps will also do the job, but I like Documents because it’s also where all my documents live.