Open the Files app and locate the files you want to compress;
Tap the "more icon" in the top-right corner and hit "Select" to choose your files;
Click the three-dot icon in the bottom-right and select "Compress".
For a single file, you will see a ZIP file with the same filename saved to that folder. If you selected multiple files, a ZIP archive named Archive.zip will be stored in that folder.
To change the file name, tap and hold on the ZIP archive, then select "Rename".