How to factory reset a 2010 MacBook Air?
The Macbook Air should have shipped with a small USB drive that contains the installation software.

It won't be easy to do what you want to without booting from something other than the System disk in your Mac.

Assuming you have the USB drive that shipped with the Macbook Air (you should have unless there is a good reason why you don't have it), you should insert it and boot from it, by holding the option (alt) key just after you hear the chime when turning the machine on.

After holding the option key for a short while, you will be presented with a choice of boot volumes, one of which should be the OS X installer.

Run the installer and follow the instructions to reinstall the OS, at which point you should be given the option to wipe the current install and start fresh.

If you want extra security, you can use the Disk Utility while in the installation mode, by choosing it from the Utilities menu that is at the top of the screen.

From there you can erase the disk, choosing from a range of security options when doing so.

If you don't have the USB drive you will have to obtain one somehow - which may mean taking the Mac to an Apple Store.

Failing that, maybe you'll be able to acquire a install disk image from some place on the web and install it to an external drive that you can boot from. Not going to help with that though.