You don't need a password to erase and reinstall OS X (which you should do with a Mac, and you don't know how the software might have been mistreated. )
You'll lose all files and third party software that might have still been installed, but you'll end up with a fresh OS X system, same as out-of-the-box new.
Start up the "new" Macbook Air, while holding Command + R.
Choose Disk Utility, from the menu that you get.
Choose your hard drive, and click the Erase menu.
And, continue with erasing the hard drive.
When that completes, Quit Disk Utility, and click Reinstall OS X.
You'll need to be connected to the internet to complete the install, which will restart automatically, and take most of an hour before you can use your Macbook Air. You'll go through a short set up for your user account, and you're back in business
(Hope it wasn't a stolen system 😀 If you can't do ANY of this without it asking for a password, then you may have an EFI password set, and you have to take to an Apple service center, or a "genius" to clear that - there's no other options.)
