I recall winning a small tournament in the early 90's and putting my winnings back into my game, so I booked a lesson with Dan Louie. Knowing I needed more knowledge of cueball path using more than 1 rail, I asked him what happens after contact with multiple rails and he said, "Shoot a million of them and you will find out."
At the time, I thought that was what I was paying him for...just tell me what happens. In retrospect, I see what he was saying. It just takes lots of practice.
When I practice, many times, I can one or two stroke a rack. Totally by feel. When I am serious, I take more time, but just saying I do not need much time to take the shot.
Before addressing the ball, I look at the 3rd and 4th ball to finalize how I will hit my object ball...what speed/power, what english, what stroke, and which side of my 2nd ball I want to be on to achieve shape on my 3rd ball for the 4th.
Like someone mentioned before, when you are learning to read, you sound out each letter, then each syllable. After mastery of reading, you can have letters that make no sense inside a word, but as long as the beginning and end are recognizable, then you will be able to read the word.
The same holds true for shooting. Rarely do I need to go sight a ball, unless it is an extreme angle or close to a rail. When I am down on my shot, I have already decided all the things I need to do from the paragraph above, then adjust my aim depending on any english. So I get from A to Z cutting out a lot of things beginners need to do.
I can actually just line up my cue and know where to hit the ball. Does it work all the time? Obviously not.

Lack of practice means it takes longer to get into that mindset, and also means that there may be more missing at intermediately hard shots, whereas if I am playing all the time, those come easier too.