Do you have ANYTHING on your MBAir that you want to keep? (pictures, music, movies, your own documents, or apps that you want to keep?)
If not, then it's simple.
Boot to your recovery system (Restart, while holding Command-R)
On the menu screen, open Disk Utility, then choose your drive, and Click erase. (remember, erasing means you lose everything that is not already backed up).
When that finishes - only takes a few seconds - your drive is erased. Quit Disk Utility, then click Reinstall OS X.
It will download files needed to reinstall the OS X system, and will take anywhere from 15 minutes to 1 hour, mostly depending on the speed of your internet connection. It will then boot to the new user setup - the same as when your MBAir was new. If you want to upgrade to Yosemite, Go to the App Store, choose Yosemite to download, it is free, so no charge for a download of Yosemite. Going through the App Store also gives you the most recent update to Yosemite.
So, you wait some more to let Yosemite download, Run the install, and there you are!
That's one way - and takes longer to complete.
Here's a shorter method to erase, to install Yosemite on the first step.
Download the Yosemite installer first. Use one of the methods to create a bootable Yosemite installer on a USB flash drive.
I like to use the good app called DiskMakerX. It lets you easily make a USB installer partition or drive, without needing to use the terminal for anything.
Boot to that flash drive.
Erase your MBAir boot drive, then continue with the OS X install. It will be much faster, because you don't need to wait for anything to download through your internet connection (it's all in the installer!)
And, you will eventually see the new user setup...
