The simplest AM demodulators are nothing more them a diode peak-detector. I think this is a pretty informative explanation.http://www2.eng.cam.ac.uk/~dmh/ptialcd/trf/trf.htm
I don't think there is a simple informative circuit or explanation for FM. I know that I can't explain it very well. FM starts with a base frequency (e.g. 105.9 FM). If there is no sound the frequency will be constant. The audio signal causes the frequency to shift higher or lower (instead of making the amplitude higher or lower). This makes for better signal reception (it doesn't get louder when you are closer to the transmitter) but also makes the receiver more complicate. All FM receivers have some kind of frequency tracking circuit that is a little 'slow' to respond. If the current signal is at a different frequency than the tracked frequency the difference is detected and converted to a voltage. I'll be honest with you, I understand them in concept, but not in enough detail to make one myself or explain it.