To start off, I want to emphasize that League is an incredibly complex game. The problem many people face with the game is that they don't know any more ways to improve and then look up ridiculous videos like „These 7 tips will help you get to Diamond“. This guide will not instantly make you diamond, but it will enlarge your knowledge of the game and give you a chance to become better at it if you practice these things a lot.
Kiting
It's the most important mechanic of the game - kiting. For those who dont know what I mean by kiting, kiting is to move in between your basic attacks. This can be helpful for ranged champions as well as melee champions. For example: If you are a melee champion and you are trying to chase someone, your are better off when you move in between your basic attacks because otherwise your champion will stand still instead of moving towards the enemy champion. Also when you are getting chased it can be a huge advantage. When a melee champion is moving towards you and you kite him instead of standing still while basic attacking or running away, you will do the same amount of damage and also keep distance from the enemy melee champion so he can't hit you. It's also possible to kite jungle camps. This is super doable due to the low range of the monsters.
Warding
Believe it or not, warding makes a huge difference. It's essential to always have one control ward in your inventory and one on the map. This gives a huge advantage because you know when you will get ganked and you know if the enemy laner has warded. This is really convenient for your jungler because he will have a way bigger chance in ganking successfully. Not only the fact that you ward matters, but also where you ward. You shouldn't ward the bushes on your lane that often, only occasionally. The tribush and river bush have a way higher priority then all the other bushes. As a jungler it's a good idea to have vision on the enemy buffs and your own as much as possible.
Map awareness
If your map awareness is crap, there is no advantage is warding, especially deep warding. Looking at the map between every CS is the best strategy. This will cost you a lot of farm in the beginning, but after you will notice hostile and friendly ganks way earlier. The main advantage of teleport is the ganks you can perform with it on bot lane. This requires excellent map awareness and good communication. As a jungler map awareness is a big part of your game. You need to gank the lanes that are pushed in and the only way to know which lanes are pushed in is through map awareness. Playing jungle is a very good way to improve your map awareness because you are forced to keep an eye on the map all the time.
Peeling
This is definitely one of the less known terms. Peeling an enemy is forcing that enemy away from its target, or forcing the enemy to not be able to reach its target. For example: Alistair peels an enemy Irelia from his Caitlyn by using headbutt. This becomes crucial in the higher elo's and isn't much of a deal in bronze and silver. It's important to have at least one crowd control tank in your team to peel for the bot and mid laner. If your team doesn't peel all the squishy teammates will be taken down by the assassins and tanks/bruisers and after that you will be easy to kill off because the is no damage left on your team.
Creep wave management
Listen carefully, because this is where it gets really advanced. Understanding creep waves is a truly hidden gem that is not utilized to its fullest by the vast majority of players. Creep waves follow a set of rules that allow you to predict there movement with just a glance and we know when something becomes predictable it can be used to our advantage. Let’s go over the basics first, to start creep waves spawn every 30 seconds with six minions three of whom are caster and the other three melee. Every 3rd creep wave that spawns will have a cannon minion added to it. This is a really complex part of the game so we will only discuss the basic 'even minion' rule. The side which has the most minions with the most health will push further until stopped by an enemy champion or tower. This can be used to your advantage, because when you are winning your lane, you can let the enemy push the wave into your tower by only sucking the last bit of life out of every minion. This results in an easy kill or an enemy champion that is zoned away from his farm. In both situations you will gain a gold advantage which will result in a lane that's even easier. You can do the same when you are losing your lane or your champion is more of a late game champion, like Nasus. You will be able to kill your minions without the enemy laner killing you.