If you're new to revolvers, be sure to use proper hollow ground screwdrivers. Brownells sells screwdriver bits specifically designed for S&W revolvers. Don't use standard screwdrivers from the hardware store because they can slip out of the screw heads, causing damage to the screw heads, and scratching your frame.
The screw under the cylinder is what keeps the yoke attached to the frame. Be careful when removing this screw because it has a spring and a detent inside. After you remove this screw, if you open the cylinder, you'll be able to slide the yoke forward off the frame. Then you'll be able to slide the cylinder rearward off the yoke. Try not to drop the cylinder, or you might bend the extractor rod. Keep the screws separated and don't mix them up.
Never pry the slide plate by sticking a screwdriver underneath. That can damage it. Instead, tap the grip area of the frame with something made of plastic or wood (like the handle of a screwdriver) until the side plate pops loose. Note that when the side plate pops loose, it may fall. So don't do this over a concrete floor. Also, don't lose the hammer block safety. Be sure to position the hammer block safety in its proper place when you reinstall the sideplate.
Never pull the trigger with the mainspring under tension while the sideplate is removed. That can damage the studs that the hammer or trigger pivot on, especially on an aluminum J frame. I'm not sure if it would damage a steel k frame, but I wouldn't risk it.
When removing and reinstalling the rebound slide, work with the entire gun in a gallon sized ziploc bag. The rebound slide is under considerable spring tension, and you don't want to lose the spring. Reinstalling the rebound slide can be very difficult if you don't have the correct tool. Brownells sells a tool specifically for removing and reinstalling the rebound slide.
When reinstalling the side plate, if it doesn't slide in evenly on all sides, don't force it by tightening the screws. Instead, remove the side plate as described above and check to see if anything is out of place. It's possible that the hammer block safety may be out of place and need to be repositioned before you try reinstalling the side plate.
I agree with the post above that a lot of range time will naturally smooth out the trigger for you.
Older S&W revolvers had 2 pins at the rear of the cylinder, and 2 corresponding holes in the extractor star, which ensured that the cylinder timing was correct by keeping the extractor star rigidly in place. That's because the hand in the frame interacts with the ratchets at the rear of the extractor star every time you pull the trigger.
Current S&W revolvers no longer have those pins. So if there is no ammo nor snap caps in the chambers, the extractor star can fit loosely in its cutout in the cylinder. So if you dry fire, be sure to use snap caps to keep the extractor star in its place.