If you have downloaded the Install macOS High Sierra.app and it appears in your Applications folder, it should
be 5.23GBs in size.
What did you do next, did you follow the instructions in this article,
How to create a bootable installer for macOS – Apple Support
if so you should have created a bootable USB installer.
When you then plug this bootable USB installer into the MacBook Air did you Restart it
while pressing and holding the option/ alt key. After a couple of minutes you should see the
Startup Manager where you select the bootable USB and press Return.
The USB should boot up where you will see a Utilities panel where you use Disk Utility to
erase the macs Disk, and then use Install OS to install High Sierra.