The positive lead from the battery goes to the positive lead of the servo. The negative lead from the battery goes to the servo and to ground on the Arduino. The control wire of the servo goes to a digital pin on the Arduino.
It's a pretty simple circuit, really.
Then, use the Servo library, and some of the examples, to make the servo move.
Making it play a drum is a simple matter of using Servo.write() with the correct values, with the correct intervals between the Servo.write() calls.
OK, so it's not really simple.
I'm testing a few ideas from my final university project
What field of study?