This is much more of a placeholder and a summary than anything; the meat of this post will be spread over a number of posts. But I couldn’t figure how to lead into this point without extending any articles on the subject far too long.
Almost everything you can do to improve is about respect. Of course, there are mechanical steps you can take to get better. But ultimately, most decisions in the game are about knowledge and respect.
It’s not enough to know what your champion and the enemy champions can do. You have to respect those options.
I’m going to start with a pretty simplistic example: Malphite. Malphite’s ultimate allows him to start a teamfight, anywhere and anytime. And the range is incredible! If Malphite has flash and his ult up, and you can see Malphite, he can start a teamfight on you. So if your top is split-pushing, and Malphite flashes and ults you, you can’t say ‘he flash-ulted me! There was nothing I can do!’
You died because you failed to respect Malphite’s capabilities. You forced your teamfight to give an objective because you didn’t respect Malphite.