Dry fire practice is the key. Get some snap caps (I like A-Zoom) and set aside a few minutes every day for dedicated dry fire practice. As you get used to it, you can increase your practice time.
If you're trying to shoot faster, forget staging the trigger. I'd also suggest that pulling straight through is better overall. The goal is to be smooth and consistent while pulling the trigger quickly. Doing so will actually disturb the sights less than pulling slowly. But the key is smooth and consistent. No start-stops, no hesitations. When you can do that consistently, then slowly build up speed. You have to walk before you can run.
The trigger return is just as important, IMO. It should be the same as your trigger pull, but in reverse. The goal is to establish a consistent rhythm. As your skill and hand/finger strength improve, you can speed up the rhythm.
Speaking of strength, increasing the strength of your hands can help. Dry firing will do that, but you can also use grip strengthening tools. I like Captains of Crush grippers and elastic bands for strengthening the opposing muscles. You can also use tennis balls or crumple up a newspaper in one hand. If you lift weights, you can do forearm curls with dumbbells or farmer's carry with plates. Don't overdo it, though. Start light and build up gradually. It's easier to overstress and injure your hand muscles than larger muscle groups like quads and biceps.
Like UncleEd said, grips that allow you to maintain a solid, consistent grip on the gun is important. That could mean changing your grips or possibly using a smaller K- or L-frame gun.
The best way to improve, though, is to seek the help of a good instructor, especially someone who knows how to run a revolver. They can see what you're doing and offer corrections and suggestions for improvements specific to you. Just one hour one-on-one with a private instructor can be useful.
In case you didn't notice, I said the word "consistent" a lot. There's a reason for that.
Just my opinion.