I just upgraded to a new MacBook and my wife is inheriting my old MacBook Air. How can I change the her MacBook Air to now be fundamentally hers? That is, so the House Icon under Users folder is her name and not mine? Also the default AppleID for purchase

You do not mention it, but I will assume you are running OS 10.9.1.

Go to: Apple menu / System Preferences / Users & Groups. Click the padlock and enter your password.

Click the + (plus sign) and set up a new account for your wife. You have to enter a bunch of info. And then create the correct Login Options. Automatic login does not require a password from the selected user.

When that is done, verify the account works by restarting the computer and login as your wife.

Make sure that any applications in your own Users folder that will be needed are moved to the Applications folder in your wife's Users folder.

Now go back to Users and Groups, click the padlock and authenticate, select your own account, and hit the - (minus sign). This step cannot be reversed, so you might want to wait a few days before doing it.

When your wife is logged in, the App Store will know.