How do I see the computer on the tv monitor with Apple tv set up?

Turn on home sharing on both the computer and ATV.

You wont see it called Macbook Air... you will see it called computer on the ATV

From there you can access some content that is on the computer like movies, music, photo, home movies and so on.

http://support.apple.com/kb/ht4620

If you are attempting to mirror make sure sure you meet the requirements (2011 or later MBA, running 10.8 or later).

http://support.apple.com/kb/HT5404?viewlocale=en_US&locale=en_US