How to reinstall OSX on a Macbook Air whose screen is broken, and OS has been erased?
There are several options:


Plug in an external monitor and then you should be able to follow the install process.
Target disk mode, but as it's a MacBook Air this would be dependent on having a Thunderbolt port, that you can connect directly to another Thunderbolt port, or a Thunderbolt to Firewire adapter into an older Mac with Firewire.