There are basically two paths. The first is to just play a ton, like the person who mentioned 1600 normals recommends. The other, and the only real option if you're already played a ton of games, is to become more self aware.
There are lots of ways to be more self aware, and the core is observation and analysis. Observation is hard when you're playing, so try out something like replay.gg or recording streams of yourself (or both). Doing it after every game might drive you crazy, but if you play 3-4 games in a night, or if you lose 2 games in a row, it can be nice to take a break from the intensity of playing.
When you're observing your old replay/stream, now is the time for analysis. Watch yourself, your opponent, and the minimap constantly. Ask yourself questions related to things that are generally good advice, like what Nameless Voice posted.
- "After that team fight, I ran after a low enemy champion. Would it have been a better choice to take an objective?
- "Was I watching the minimap often enough while I was extended? My ward caught the enemy jungler about 8 seconds before I started moving to safety. Maybe I could have lived there if I was checking the minimap more frequently while extended."
- "Am I overestimating how much damage I can do? I tower dived the enemy 3 times and each time she survived with at least 100 hp."
- "Was that trade worth it? Was the amount of damage I inflicted worth the damage I received and the CS I missed?
"Who to play? What lane?" - Pick a small number of champions for two roles (since you need to select two roles in queue), maybe 2 each. Ideally they play different team comp roles (i.e. if you like Braum, maybe your second support should be Janna or Zyra rather than Tahm Kench or Alistar). You'll need more than 2 each if your picks are popular (other team might pick first) or frequently banned. Support's a fine role to main, and you'll get faster queue times and the knowledge that you're helping out everyone else's queue times too :)
"Dealing with counter picks?" - Don't stress out over them! Many reasons for this.
- Just because person A tells you it's a counterpick doesn't mean it's effective. It could just be that he played that matchup before and did really bad, and he blamed it on "being countered".
- Lots of people put so much emphasis on counterpicking that they'll play champions they don't know well at all just to counter you; this gives you a huge advantage because champion experience is so much more important.
- Some people sacrifice their own team composition in order to counter you. If the opponent picks an assassin when their team could use a tank, then the rest of your team can frequently take advantage of that (even if you're behind personally).
- The more you play against perceived counters, the better you'll get at playing against them. You'll know exactly what they can do and when, which will help you play against them. When combined with the previous points, this can really wreck the enemy team; if they're not even gaining the lane advantage expected against you, then sacrificing personal experience and team composition is a HUGE loss for their team.
Lastly, based on other parts of what you said, you should remember that there are many paths to being successful at League. I'm a support and jungle main because my mechanics are terrible. I can't hit even 90% CS in custom games unless I'm using someone like Annie, and I lose 1v1s in most matchups even when I'm ahead. I'm Gold5, and it's quite possible I'd lose to you in a 1v1 lane matchup. That's because my strengths lie in other areas; I know how to be a good decoy, my macro awareness is good, I'm a reliable shotcaller that can get people to follow my suggestions, and I have a pragmatically positive attitude in game.
The important part of this is not to view KDA and CS as competitions, particularly in game. It's one thing to say "Hey team, Orianna killed me 3 times in lane and has 50% more CS than me. We can't team fight unless we catch her out first." That's productive. Saying "I shouldn't listen to this person because I have a better KDA" is not productive. I'm not saying you should listen to everyone who offers unsolicited advice; just make sure you don't tune them out simply because your CS is better.