The NRA Bullseye Course...
Requires thirty shots fired "Rapid Fire".
At 25 yards, one must shoot the pistol off hand (standing and one-hand only without support) at a three inch target. One fires six strings of five shots in ten seconds each.
Simply doing it is instructive.
Without disagreeing with any of the previous answers, the answer is two-fold.
The difference between a clean 'slow-fire' shot and a clean 'rapid-fire' shot is simply one of interval. The amount of trigger movement is minor. One strives to be 'smooth'; which is independent of 'speed'. Work on the slow fire trigger activation. When you can fire good clean single shots, then move on to doubles. The motion of the finger is the same - it's just a little faster, not abrupter.
Practise. If you can find a regular Bullseye match in your area, shoot those matches. You will find an increase in dexterity and therefore, trigger control builds rapidly. This is that 'muscle memory' one hears about so much. It's just practise and practise until it becomes ingrained in your nervous system.
The skill applies to all forms of shooting.