Japle has offered an excellent opinion on dry-firing practice. the only thing I will add is always unload the firearm to be used in a different area or room than you will be dry-firing in. Don't ask me how I learned this lesson.
That's the truth! I managed to set off a Ruger .22 pistol in my off-campus apt in college. That gun was NOT loaded. I had checked it. Then I got distracted and put it down for a few minutes. When I picked it up again, it had loaded itself.
That was over 40 years ago. Since then, if a gun leaves my hand, even for a second, I check it.
Trigger control:
There are three basic ways to pull the trigger.
a) Line up the sights and as soon as your sight picture looks perfect, close both eyes and yank the trigger. This is the most common technique I see at the range.
b) Line up the sights and as soon as your sight picture looks perfect, start the trigger squeeze. When the sights wander, stop squeezing and get that perfect sight picture again. Resume your trigger squeeze. Repeat until your eyes blur and you run out of air and start shaking. When you can't take it anymore, close both eyes and yank the trigger. Also a very common technique.
c) Line up the sights and as soon as your sight picture looks perfect, pull the trigger straight back smoothly, with no hesitation. When the gun fires, the sights may have moved a little, but the shot will still be a good one. With practice, you can compress your trigger squeeze into shorter and shorter times.
This technique is pretty rare, from what I see at the pistol range, but is normal among top steel shooters and others who need to shoot fast and accurately.