"How do I shoot faster" is probably the most commonly asked question in action shooting. A lot of people say "practice", which is good advice but only if you know what to practice. A more complete answer would include an examination of what techniques will help you shoot faster.
1. The first item that will help you shoot faster is to develop your recoil control skills, which are primarily a function of your grip and stance. For stance, all of the top competitive pros use the modified isosceles stance, which keeps your knees soft (bent) and your body "forward" so you're "on the gun". The second component of recoil control is your grip. Todd Jarrett likes to say "grip the gun 20% tighter", a technique which (I think) Mas Ayoob refers as the "crush grip". To establish your optimum grip pressure, hold the gun in your firing grip and grip the pistol until the front sight starts to bounce and shake from your grip pressure, then relax your grip until the sight stops bouncing rapidly - that's your "ideal" grip pressure for rapid shooting. The 3rd aspect of recoil control is strength - holding the gun that tight takes a considerable amount of grip strength, so I recommend looking into training exercises for your upper body/forearms.
2. The second aspect of "shooting faster" is trigger control. Your average semi-auto cycles in something like 0.06 seconds, which means that the gun is always waiting on you. When you're shooting fast, you want your trigger finger to come all the way off the trigger of the gun, and then re-engage the trigger, especially if you're using a revolver or striker-fired pistol. Jerry Miculek keeps the return springs in his revolver at an "unusually" high weight, as he wants his finger to come just off the trigger in between shots. Some guys feel like you should "ride the reset" on the trigger, which means let just enough off for the gun to reset and keep constant contact with the trigger. The problem with riding the reset is that you're depending on an extremely fine muscle skill to know when that trigger's reset, and for speed it's much easier to just come off the trigger in between shots.
3. The third aspect of effective speed shooting is the draw. Back to quoting Todd Jarrett: "If you blow the draw, you blog the string". So true. Practice your draw at home, using a "
progressive draw drill". That will allow you to up your speed on the draw in a controlled environment.
There are a lot more tips and tricks to shooting fast and accurate, however these three fundamentals never get old, and are always areas in which you can go faster.