I recommend certain youtubers who put out tutorials that you can learn a lot from. Mechanics just takes time and practice, but learning more about the game and figuring out where you are lacking is a big part of League.
Mechanically I am pretty trash. However I rose 4 rankings in 2 days based purely off my knowledge of the game and my application of it.
Pants Are Dragon supposedly does a number of tutorials although I don't know much about him. I personally am a massive fan of Scrap Computer. He puts out very comprehensive guides on just about all of League's mechanics.
He also covers how to play different roles, has some very in depth guides on individual champions, and is just a wondrous learning resource. He is also constantly updating his channel too. There can be a lot of info on it but his playlists divide everything into general categories.
Outside of guides I recommend using one of the many sites that will record games for you then watching back over them and thinking about what you could have done better.
A big part of it is just practice of course. I spent a week doing cs practice. Aka playing 6 10 minute custom games a day with a variety of challenges in increasing difficulty. Before moving onto the next game I had to hit 85% cs rate in the current difficulty. My in game csing practically doubled, for a long time I was actually hitting around the cs levels of the Master tier average just because I spent so much time focusing on it and I have a really good eye for watching all my minions and tracking their damage. I honestly need to go back an do it again because my csing has been pretty bad lately.
A guide/results can be found here: https://www.youtube.com/watch?v=xfmm40Ow-T8
Although due to minion spawning time changes the actual expected/max ccs numbers are a tad bit off.