Does the person you are calling have a webcam?
Depending from which device (computer/laptop/iOS device) they are calling, your calling partner may have to activate the Video camera manually. For example, Skype for Mac doesn't seem to automatically start a video call, even if you have the camera enabled on the iPad. The other person also has to activate video call, otherwise you will only see yourself.
Anyway, if you can let us know, from which device the other person is calling, we can easily solve this case.