Sign into the App store.
Download the macOS/ OS X version you want to install onto the Air. It may be listed in your purchases if you need an older version.
When the download completes quit the installer - you do not want to install it on that Mac.
Now follow the Apple's guide I posted above or use diskmakerx.com - it is a simpler process to use that app. It will copy the installer files to the USB disk.
Insert the USB disk in to the Macbook Air.
Boot it whilst holding 'alt'.
Select the orange USB disk to boot from & then run through the installer as normal.
NOTE: It can be tricky to get certain older versions form the App store if the Macs are different ages, post model info & the versions of OS X you want to install if that applies to you.