Small Mistakes Add Up
While watching LCS games, have you ever noticed that you don't see what they're doing that you don't? That's because most of the differences are small things that add up. In this game, there are small things people do that add up to a very big difference. I'm thinking most people don't realize that what they're doing is even a mistake, so here's a few common mistakes off the top of my head, and if this post gains traction I'll add to it from the comments, with due credit of course.
Sitting at your turret/camp at the beginning of the game. There are 4 entrances to the jungle. That's 4 ways for the enemy to screw over your jungler so that when you need a gank they're 3 levels behind. Ideally, you'd have 1 person at tribush, one person in the river bush behind blue, 1 person in the bush behind red, and 1 person in the other tribush. That even leaves 1 person to goof around. You might think it's a waste of time because invades are rare, but ask yourself this: do you have anything better to do before minions spawn? Go walk into vision range of their turret? Sit in the furthest bush in top or bot to try to get off an surprise level 1 kill (which hasn't worked since your account was level 13)? You don't need to miss a single minion, just stay in that bush until the minions are at the inner turret by which time an invade is unlikely.
Going to a lane that's already being covered/grouping up with a split pusher. In laning phase, you'll return to your lane; that's a given. But after that, if Wukong is already on his way bot to defend the turret, Ashe needs to stop pinging 'On my way' and just go somewhere else. You're removing a lot of pressure from the map that way. And at no point in the game, even during laning phase, should you teleport to a lane someone is covering. That is such a waste of a summoner spell. Along the same lines, if Tryndamere is split pushing, you need to go to your team, and your team needs to stay the hell away from him. It's bad enough one member of your team is missing from a possible team fight, you'd make it a 3v5. And Tryndamere doesn't need help pushing, he needs help keeping enemies away from him. Your job is to give the enemy a reason to stay where they are instead of 5 man ganking him.
Trying to carry when you're clearly behind. This actually isn't a small mistake, it's a huge one. Your playstyle should change based on how the game is going. If you're not doing so hot, you need to set your ego aside. Even if you know for a fact you're the best player in that match, if you're 1/4, you're not gonna carry. Don't try to kill the 4/1 Riven you fed, don't ask for a buff (buffs don't help you when you're behind; they make you a juicier target and when you respawn you have to fight someone who has a buff), don't flame, don't try to make #LCSBigPlays. Just play safe and play around your teammates. Fulfill the role your champ is best at, but do so without unnecessary risk (landing Lux's snare isn't worth getting hit by Blitz's hook). Buy defensive items (any role, not just tanks/fighters). I have a friend I play with who was getting dumpstered. He's a mastery 7 Ekko main, and I know he's good. But one game he was behind after being camped, and kept playing as if he was ahead. He died over and over, and blamed everyone else for not diving in with him... which we didn't. I didn't try to support him plays because he wasn't making the plays, it was bot lane iirc, with top and I playing off of them. We came close to winning fights like that, but because my friend would jump in first as if he was even remotely capable of doing damage or escaping, it was an uphill battle. If he'd made decisions based on bot lane instead of going in and expecting everyone to support him, we'd have had a chance to turn the game around.
Not playing objectively as a jungler. As a jungler, your only job is to control the map. That is the only thing you are tasked with. Anything that is not your team's turret is your responsibility. So if everyone is going to dragon and you're trying to hold top, ya done goofed. Literally anyone on your team can hold top, but only you can smite dragon. 25 minutes in your team is headed to Baron and you want to back because you still only have a Hunter's Talisman? Too bad, you need to go over there to help secure it, while making a mental note to never play Warwick again.
You gave up. No matter how bad the game is going, there's a chance to get it back by playing safer and smarter. You've watched your team throw so many times, how can you not believe the other team can and will? You may think you're still trying, but if you analyze your gameplay and your attitude, you'll find that you're really just going through the motions. You should adopt the 'Never Surrender' policy. Some people say it's a waste of time, but mentally it's not. If you refuse to take your one chance to get out of this game, it forces you to actually try to win.
You die too often. One thing guides usually don't cover is how important your death is. Go compare the team kills from your last 10 games to the team kills from a high ELO game. Getting better at League doesn't mean getting more kills, it means having less deaths. That leads us to a very common misconception: it was worth. Let's say at the end of laning phase you're 23/17/2. You're really fed. You know who else is really fed? Your 18/25/1 opponent. And unless you tunnel vision onto them every single fight, even at the expense of your own life, they are going to tear through your teammates. There might not even be a way for you to stop it. For example, let's say you're Brand against Lux. No matter how fed Brand is, he can't stop Lux from decimating his team because they're both back line mages. You would have to walk straight into their front line just to get to her. It's better to end the game with no kills or deaths than to take turns feeding. Unless you're against Teemo. Edit: Just learn to farm safely. If you can be 20 farm ahead of your opponent, that's about one kill worth of gold. So you don't have to go for that tower dive play, just let them back and farm.
As I said there's tons more, but that's all I have for now.