Everything down the slightest reaction the pros exhibit has been learnt, practiced and drilled into a masterful level.
You may think of it as a stimulus-reaction sequence. When a D-men moves along with you, coming forward, he adjusts his speed, angle and stick position accordingly to little hints you tip him off with on your body. The basic hint is your shoulders area. A guy who has played enough hockey will recognize the movement from its origin because he has been brought into seeing it as the origin of a given sequence. So, you have seen the sequence of movements required to go from a point to an other and you will adjust as soon as you understand this is the sequence of movement which will be pulled off.
A stickhandler will be able to hold on these hints to the very last moment, produce some purposely, exaggerate others and literally use his entire body to fake you into going just enough out of line so that he has the space to go. Same for shooting, passing and, at the opposite, preventing these plays. So, yes, it's learnt and anyone who tells you otherwise simply doesn't know what psychology is.
Now, how do you teach that? All training systems are meant to bring the player into doing something he's barely able to do... you need to build up the skills in a way that will keep your pupil (which may be yourself) into a constant mentally demanding state: he must think it out. If you can pull off the session without thinking about it, it's not hard enough - like weight lifting, you got to keep yourself into the effort zone and skills are mental. If you go too far, you're able to process all of the information given that you need to be focused on too many things; if you don't get far enough, you'll do it without giving it a mental effort.
That's also one of the main reasons why so many kids seem to never get good at something: you have them try something too hard for them, or too easy for them. When you first picked up a hockey stick, after ten times at the rink, you probable made insane progresses - imagine improving that fast or nearly that fast over ten years... that's the point of this theory which is called "concentric circles of learning."
More specifically to hockey sense...
It's a pattern recognition accompanied with an early, fast and coherent action that puts the player into a favorable situation and/or position. The first thing you would need to do is take your player into a situation which fits his/her role and, then, you need to literally tell your player what to look for and drill it a couple of times until he gets some ease.
Start by giving the play fewer dimensions than the real game situation - instead of making the Dmen cut the shooting line, the passing lines and the skating lines in all directions by requiring of a young skater to be perfectly place, start by having him guess on two options and tell him/her what will tip off which play will occur.
When the player shows more ease, change situation - give two different options. Then, add a third. By the end, mix all of these sequences of possibilities and see if he can react properly. Remember also that reinforcement is important and that punishment is likely to be misinterpreted by your subject. So, instead of being discouraged or something, begin by rewarding with words and hand claps each thing the player does that tends to get him/her nearer doing the right thing. As the player progresses, become more demanding, but still be rewarding.
After a while, your player will have been drilled into many situations and, instead of seeing them randomly in a game where pressure and lack of skills can worsen his/her abilities, he will have coherently associated appropriate reactions to given plays. That's like skipping years of game time...