First of all (and take this as a question, not an insult or something, I don't know your exact application), if you want the jaw to move, I assume the sound it moves to comes from the animatronic itself. So why bother using a microphone, just wire the ADC to the Audio-Out, it is HIGH-Z so it wouldn't have any effect on the signal.
Now, to try to answer your actual question: If you have what I would consider a sound-sensor (so effectively a more sensitive clap sensor), you will just have to write a loop polling the sensor-out and writing the corresponding state to the servo:
while( true )
servo.write( digitalRead( soundSensor ) ? 90 : 0 );
This is, of course, very inefficient and will only work if all you do is move the mouth or you have a relatively fast main loop. However, I don't know how far you are in your journey through Arduino coding, so I just used the simplest example I could think of. If you want to do it properly, look into interrupts.
Also, please try to give more information next time you ask on this forum. The more you tell us, the better we can understand your situation which means faster and better answers for you.
I hope I could help. Happy Making!