The black magic of PID comes in when we talk about HOW it adjusts the Output to drive the Input towards Setpoint. There are 3 Tuning Parameters (or "Tunings"): Kp, Ki & Kd. Adjusting these values will change the way the output is adjusted. Fast? Slow? God-awful? All of these can be achieved depending on the values of Kp, Ki, and Kd.
So what are the "right" tuning values to use? There isn't one right answer. The values that work for one application may not work for another, just as the driving style that works for a truck may not work for a race car. With each new application you will need to try Several Tuning values until you find a set that gives you what you want.
Note: there is also now a PID Autotune Library that can help you determine tuning parameters.