Minimum Resources to Download / Install OSX on MacBook Air

Usually nothing is required to install macOS except an active WiFi-Router connected to the Internet with DHCP enabled and its WiFi password.

After turning on the Mac and immediately pressing ⌘ cmdR the MacBook Air should boot to macOS Recovery over the Internet (earlier "Internet Recovery") (Apple Support: About macOS Recovery). You will be asked for a WiFi password.

If macOS Recovery over the Internet works you should see a spinning globe and depending on your Internet speed you will see the Recovery console sooner or later.

The console contains several tools including Disk Utility and Reinstall macOS

Disk Utility is required to partition and format the SSD. Later choose Reinstall macOS to install a new system.

If the above shortcut doesn't work you can try to press and hold ⌥ alt/option⌘ cmdR or ⇧ shift⌥ alt/option⌘ cmdR at startup.

The different boot and install options are outlined here: Learn more about these key combinations.

To improve user experience I would ask the future (unexperienced) user which system he/she/* would like to have and simply download and install it up to the configuration screen (like Apple does with new Macs).