How to find maximums or peaks of sound

Rather than a microphone you might find it easier to use something like the Sparkfun Sound Detector board which already does the basic integration for you and has an output which follows the overall volume of sound. Because that is a lot slower moving than the actual sound waveform it's easier to deal with. Have a look at SparkFun Sound Detector - SEN-12642 - SparkFun Electronics? and the associated tutorials.

Steve