It takes a long time. Honestly--you just have to enjoy the process over hundreds of games. Take time playing every champion and learning their skills, damage, and cooldown. Their mechanics. Then when you play against them, you'll know it better.
There's no shortcut. It's just a game that requires a ton of knowledge.
It's why me, a previous top 200 player from S1-S3, I play now and I'm gold.
I know my mechanics are rusty. But there is just so much knowledge I don't have now. Damage values, skill descriptions, how different champions work, cooldowns, etc.