In my mind, trigger control is the holy grail to achieving higher scores in Bullseye shooting. Virtually everything else done in shooting is easy by comparison. As you read these next sentences, please keep in mind that I am making a comparative statement...
Stance is easy, we call all stand fairly still
Aiming is easy, we can all point the gun at something and keep it in the sights
Breathing is easy, we do it all the time
Cadence is easy, we all walk at our cadence
Holding the gun is easy, we can all pick up and hold a gun
Pulling the trigger without affecting the point of aim is difficult, very difficult. Our trigger finger is a pretty strong digit and, unfortunately, the rest of the hand wants to follow along with the motion of the trigger finger.
Before we continue the discussion on trigger control, you should read the topics on: Stance, Aiming, Breathing, Cadence, and Hold. You must be comfortable in understanding how those affect your ability to shoot.
As you can tell, there isn't much to the other physical tasks that greatly affect your score so the last physical thing is trigger control. The bad news is that it is very difficult to develop a good trigger finger.
As mentioned elsewhere, one of the least expensive ways, and perhaps best ways, is with dry fire practice. You must be able to pull the trigger without altering your point of aim! During live fire, even with the training targets, you may not see the small changes in your point of aim which is why there are benefits to doing the dry fire. The few times I do it, I can instantly see what happens when the trigger breaks and the hammer falls. You have to first train yourself to see that cause and effect - don't blink and watch the movement. Then you must try different things to get a clean pull on the trigger.
You can change your hold on the gun. By holding the gun a different way you will get a different motion out of the finger.
You can change what part of your finger rests on the trigger. I was taught years ago to put the pad of the finger on the trigger. More recently I have been using the inside knuckle of the first joint, but this only works for the 1911.
You can change the speed with which you pull the trigger. You might be doing a pull-stop-pull-stop method of trigger control. I often fall into that problem and have to work my way back out. You want to pull the trigger as one continuous motion.
You can observe your trigger finger and see if it rests on the frame of the gun and the trigger. Generally this isn't a good combination. You want your trigger finger to only touch the trigger.
You can purchase an air pistol to help develop trigger control. I have several and use them at different times. One is a single shot, pump action target air gun with a good trigger. This helped me a lot when I got back into shooting in 2011. I have another one that is a CO2 powered multi-shot gun which looks like a normal semi-auto. It has a very stiff trigger with a long pull. I use this one to help develop control for a straight back trigger pull. If I can pull this trigger back without affecting the point of aim, I will be in great shape with real guns.
Slow fire trigger control is much more difficult than sustained fire. In slow fire it is hard to make the trigger control an automated process. With sustained fire, for me it is almost completely automated. After the first shot, the remaining shots break automatically as soon as the red dot is in the black. Slow fire trigger control can be practiced and even trained with dry fire exercises. Sustained fire on the other hand can only be improved upon during live fire. But, I also know that when my slow fire trigger control is well behaved, my sustained fire performance is also good.
I don't recall who said/wrote it first, but I firmly believe in "if my sustained fire scores are good, and I am suffering with slow fire, then I know I have to work on the fundamentals". Sustained fire can hide a lot of bad stuff because you are not thinking about it as much during the actual process. So when my slow fire scores are sub-standard, I go to work on the fundamentals with most of that effort spent on developing better trigger control.
You have to be willing to accept the fact that your trigger control is not as good as you think and then put in the effort to correct it!