a lot of that stuff honestly is innate skill and not something that is learned. reaction time especially. I mean obviously league isn't a linear game different things require different actions so you gotta learn how to dodge a specific spell rather than improving your time.
a lot of skills in this game you gotta bait your opponent into missing them. such as. brand W or chogath Q. if your standing on a chogath Q even if you Move immediately same time as cast. unless you have crazy movement speed you will be hit. a lot of players in league. good ones. move around in hard to predict patterns so they don't get themselves where they walk in the direction oft he spell before cast so it becomes impossible to dodge at a certain point. you just move in a pattern and hope your not in the middle of the spell on cast because then its nearly impossible to dodge and hope your on the edge and since you've been moving in a pattern you already have in your mind your going to change your direction so you can move out of the spells range without thinking where and how . you only need to think about where.
the best thing is to always move around in differnet patterns directions in lane and not make yourself predictable .
if your for example. being chased by a blitzcrank. if u have no mobility like an ekko E or ezreal E. then you simply start going in a zig zag or a swirl. and when you hear the sound of blitz hook you simply move in a 90 degree angle. when the blitz if focused on grabbing you at the point you were at. obviously blitz an idk guess and get lucky or something but its out of your hand at that point. if your too lose he will probably land it but the further you are the more time you have to dodge the spell
and always. assume the spell is closer to you than you see. your moving in zig zags. you hear blitz hooks. sound is more important than visuals here. you immediately take a sharp direction away
point is. don't move in straight lines. dont move in a predictable patterns and you should be fine. you can't dodge everything. but you get better at it.
make the enemy try to hit you with the spell instead of him making you dodging it. if you get what am saying.
this all probably sounds dumb i hope you understand something maybe i dont know what am talking about.
the hardest skillshots to dodge are thresh hooks (because of the bullshit animation where it gives no information where the hook is going) . xerath Q and brand W in my opinion. maybe ezreal Q in certain situations too. jayce hadouken thingy. morgana q (this one is annoying). and few others