Opening a .zip file is really easy on the iPhone. If you're using the Tape Eater app, just import the file, and it will open. If you want to open it yourself, follow these steps:
Step 1: Go to the Files app and find the .zip file you want to open.
Step 2: Tap on the .zip file, and it will open by itself.
Alternative Step: If you don't want to tap the file, press and hold it, then tap "Uncompress."
Step 3: Tap the new folder that shows up, and have fun with your file!