What MacBook Air do you have, did it ship with Snow Leopard, do you still have the original installer? Most importantly, do you have an external USB optical drive? If you don't have an external USB optical drive, the cheapest substitute for the Apple USB Superdrive is one made by Samsung and sells for just over £20 here in the UK. Connect the external optical drive, insert your install DVD, boot from it by restarting holding down the C key, then first run Disk Utility repair disk option from the Utilities menu. If all is OK then restart from the DVD and complete the install.
Some Mac's, I know for sure the Mac Mini without the optical drive, shipped with a USB memory stick installer. If your MBA shipped with one too, then boot from that rather than a DVD. It's hard to be precise not knowing exactly what you have.