I grew up shooting S&W revolvers, and didn't start shooting autos until I was well into my 20's.
You have to master the trigger. That's why I think everyone should start shooting handguns with a DA revolver. Once you master that trigger, you'll find it easy to master every other trigger out there.
Do a lot of dry fire practice at home. Unload, check that you are unloaded, and check again. Keep your ammo in another room. Then, pick a spot on the wall, put a target on the wall, etc. I've read of some people looking in a mirror when they practice. Not a good thing, since you'll end up looking at your reflection instead of the sights like you should be.
Start out slowly. Line up your sights and use a slow, consistant trigger pull. Don't press the trigger any faster than you can keep your sights aligned on the target, completely through the press and break. Do this every day for about 20 minutes for weeks. You'll find that after a few days, you may be able to speed up a little, maybe not. Either way, shooting faster than you can hit your target is a waste of ammo anyway, so why build muscle memory dry firing faster than you can accurately shoot, right?
When you go to the range the next time, shoot the same way you have been dry firing. Slowly and accurately. Speed with a revolver is built up over years, not a few range sessions. Concentrate on accuracy. Once you do that, speed will come easy.
If you try to speed up too quickly, you'll find your accuracy suffers. Back off, slow down, and get back to basics. I wouldn't recommend speeding up until you have months of practice under your belt.
Dedicate the time for quality training and practice, and let us know how it works out.