Vibration and Sound measurement through LCD

I was told that for the sound portion I need to have a sampling rate of at least 40kHz (assuming I want to measure up to 20kHz, and I learned from my comm class something like fs = 2f). How do I apply it to the Arduino? Through some research I found that I need to set the prescaler to 16? How do I apply that to my code?

Quite simply you can't. The arduino will not sample analogue data that fast.