Skillshots, Mix of Experience and Innate Talent
A skillshot is an ability that can be avoided, in the same fashion a juke is the action of avoiding a skillshot.
This article will be short. Indeed the art of skillshot and juke can’t be theorised. It is quite instinctive, even though your brain makes all sort of calculations. Some people are more talented at it, but in any cases to improve this aspect of your gameplay you need to… play.
This ability to skillshot or juke comes mainly from experience. The more you play the more you will “feel” the future position of your opponent (which will allow you to hit your skillshot) or where you opponent will use his skillshot (juke). Added to that playing games with various champions allows you to know the cooldowns of various abilities. Your opponents will have the tendency to use their skillshots (for instance while chasing you) as soon they are up, if you know the cooldown you can sidestep and juke right on time.
There is also a part of innate talent. Some players will quickly become good at skillshots while some will struggle. If you are not gifted in this aspect of the game it is not as important as it may seem. Jukes and skillshots are flashy but they are only a tiny part of the game League of Legends. Also, you can easily find champions with little to no skillshots in their kit (not like Ezreal or Lee sin…).