Honestly, the elo ranking system has led to League being one of the games with the most toxic and poor sports gamers I've ever seen. There is an elitist attitude that basically pours from the top down. Players make their own teammates their enemies when they start losing and are a bigger reason why teams lose games than the actual skill of the opposing team. I quit before season one started due to the toxic players.
The game became so popular in a fairly short window of time, but it has so many flaws that have actually become worse since I returned playing in season 3. It is a team game but team work is really simply based on individual performance with this game. If teammates actually saw you as such, they wouldn't be that way. Summoner's rift has now been designed for one player to dominate the other 9...not for a team of 5 to win against another team of 5.
I'm going to be real here...the only way to learn to play this game is by sticking it out and muting your teammates. All of them unless they are friends. There will not be any real coordination if you are voice chatting so you're actually better off just muting everyone at the start of the game.
New players should start out by learning a different champions kits in games against CPU. This will help you get an idea on what style and lane position you want to learn to play. It's best to learn a little bit of all of them, but that will help steer you towards learning how to play a few you have chosen as go to champs.
Focus on laning SAFELY and DEFENSIVELY first....even though it's almost impossible to do now thanks to the season 6 balance changes where damage is so high and tower diving is now a 'safe' tactic, learning how to do that and getting CS is what will give new players the best chance to compete after the early phase.
The snowballing that is taking place now also prevents new players from learning as they aren't really given a chance to learn from their mistakes...they just simply die over and over to a snowballing experienced player so it is even more important to try to learn how to lane safely which includes predicting and warding against ganks.
After that, I'd say learn team fighting. ARAM is a great place to develop team fight skills as well as dodging, positioning, and CSing since it is so difficult there with 5 opposing teammates aiming at your face. You will develop team fighting skills much much faster there than playing normals.
As far as jungle and map awareness, the only real learning tools apart from just gaining experience for that is watching youtube videos on jungling and warding.
Learning when to be aggressive is the pretty much the only thing you can really learn through experience and this is where I find most of my teammates fail as this game isn't the same as FPS death match which many players have brought bad habits from. For example, I laned with an Irelia in URF today who lost us the game by taking a bad dive when we were actually winning lane and could afford to play safer. It wasn't simply a greedy play which happens from time to time, it was just sheer over-agression. She had been feeding non-sensically earlier but we were able to maintain until that last dive.
With that said, impatience will kill beginners in this game and it will ruin them from experiencing what this game actually has to offer if the toxic teammates don't first.