Attach the wrist cable to your wrist before you handle electronic components. Wet your wrist with salty water or lick your wrist to ensure a good electrical contact. Make sure this stays on your wrist while working on the Mac Pro computer.
You do not need to worry about getting a shock. However, do not handle mains powered equipment while grounded like this. Battery powered drills and screwdrivers cannot give you a dangerous shock and are safe to use.