If you have not already done so, shut down MBA, restart, and try again. If the camera still does not work, use all relevant suggestions from Apple's http://support.apple.com/kb/HT2090.
(Apple has changed the built-in camera's name on newer Macs from "iSight" to "FaceTime" and then to "FaceTime HD." Regardless of the name of your Mac's built-in camera, the same info and troubleshooting applies.)
If your troubleshooting proves that yours is a Skype-specific problem (your cam works in more than one user account with Apple apps) that remains even after you have updated to the latest Skype version that is compatible with your Mac OS, Skype's comprehensive support system should best be able to help you use with .
You can search or post for help with your problem in Skype's dedicated Skype Discussions for Mac. The Skype users who post there may have already solved your problem.
You're most welcome, Diana.
I am happy to read that your Mac is working after power down and restart!
We all need to restart occasionally. Restarting after a shut down clears caches and loads a fresh copy of all software. Especially because it is free and so easy, I make it the first thing to try whenever I notice any new quirk or problem.
For your future restarts, one minute after shutting down is more than long enough to wait before powering back up. However, as your 5 hour wait has proven, longer delays will work as well.
Enjoy your MBA!