A little bit of backstory, I was just like you, a (hopefully) friendly player who always just tried to stick to his gameplan and hope for the best with my team.
I've been trying to climb the ladder for years, but much to my dismay, I'd get tilted whenever my team just didn't come together and win.
It was frustrating to consistently win lane but lose games even when constantly roaming and trying to grab objectives for the team.
The problem is that there was no communication and that my teams would often just do their own thing and end up failing because there was no real leadership.
However, I've recently adopted a cute puppy and I've been watching tons of Youtube clips on dog training. I found that it worked splendidly for my dog. The whole time I've been watching the videos I thought "how could I get my teammates in LoL to behave like that?". Suddenly everything clicked for me. I've started to subconsciously use the very same dog training techniques to not only boost my teammates' gameplay but also their morale. And it works.
You see, the Average League of Legends player is much like a dog, they aren't very bright and are easily distracted, but they like to be praised and rewarded. They'd probably eat their own poop if they could. They are much more reactive to positive reinforcement than negative reinforcement and they're quite willing to please their leader (once they know who the leader is aka You).
In order to establish leadership, you must first gain the authority and respect of your fellow LoL player. In other words, you must train yourself to become the pack leader.
How do you do this?
By having a positive, strong, calm authoritative energy. LoL players are very receptive to the energy of others. Thus it is important to stay consistently calm and in charge of the situation. Of course, it is much harder to give off these energies online as they cannot read body language, however by using commanding language helps in establishing dominance.
Learn to use phrases like the following:
"Group with me."
"Run it down mid."
See, these are simple commands that come off as authoritative but not toxic. They are not negative commands, but positive ones. Rather than ask them to not do something, ask them to do something else instead. You want to avoid toxicitiy as much as possible, as it only undermines your authority and it also makes you come off insecure and mentally unstable, and dogs do not respond as well to insecure unstable leaders. When your team follows your commands or does well, make sure to praise them with phrases like "Good job!" and "Yes!". Much like dogs, LoL players love being enthusiastically praised. By praising your team often, they subconsciously become more receptive to your commands. Do not put down your teammates, no matter how boosted or tilted they are. It is your duty to instead, raise them up. Make them better and more obedient to your commands.
Another great way of establishing dominance is also by consistently winning lane. Sometimes your team is not willing to listen to you unless you prove yourself to be a good player. Thus, in order to become the leader, you must also in a sense become the best player on the team. This requires more hours being sunk into the game, more research done, and more mechanics-based training on your part.
However, perhaps you are a little shy? I was much the same way, as I preferred as much as possible to avoid leadership positions before adopting a puppy.
Leadership requires an extra duty of responsibility. It sounds like it might not be for everyone, right? I mean if you mess up and make some dodgy calls, it all falls on you. However, without a leader your team is practically bound to lose games and you cannot always wait for someone to take the reins and lead your team to victory. Thus, if you want to win games, that leader must be you. Even if you make dodgy calls every now and again (everybody does), it is important that your team has a pack leader. A strong pack leader provides moral support, greater communication, and a shotcaller. Most soloqueue teams lack all these, but with you as the pack leader you are bound to win more and lose less.
Good luck, pack leaders.