Trying to restore my MacBook Air to factory settings... how can I do this?

So, are you trying to sell it? Then follow the instructions in the link I posted.

If you just want to start over, you can do so with internet recovery - you can wipe your hard drive in internet recovery as well using Disk utility.

https://support.apple.com/en-us/HT204904

Ok, so you will need to follow these instructions - why? Because the Mac will be associated with her Apple ID and password and you won't be able to reinstall or update apps unless you disassociate the machine and then set it up from scratch using yours. Make sure you erase the drive and reinstall the original OS:

https://support.apple.com/en-us/HT201065

exactly what model/year/specs is it?

Are you getting it ready to sell? If so, use these

https://support.apple.com/en-us/HT201065