Some things Ii've noticed while trying to climb.
As I've been looking at problems I have, mainly not cs'ing properly, not using item actives (ie randuins active), and not roaming/rotating correctly are big things I've noticed. I've also noticed some of the things others just don't seem to do.
First is optimizing your build. Whether it's just what you get going into lane, or simply your item build, sometimes it just doesn't make sense. For example in one of my recent games I had a Cho top. For some unknown reason the fiora and kat switched so it ended up being a Kat to face him. Whether it's not being able to land his abilities, or more likely his extemely offensive build, he manages to lose. Now instead of building tank and just stopping her every fight, he proceeds to build damage, blowing up every time.
You see this against all ad teams where no one buys a FH, or pretty high AP teams with no locket. Simple items like these can win you games.
Second is teams give up waaaaayyy too easily, and start attacking their teamates. Something didn't go according to plan? Yelling at everyone will do nothing, even if it is their fault. All it's going to do is make them play worse, or just start attacking you.
Third is people need to start looking at what their team is comprised of, and use it to their advantage. If you have a team with Tryn top, Nid jungle, Zed mid, and some assorted bot lane, teamfighting probably isn't your strong suit. However it hurts me to see things like Maokai splitting top while his team is getting destroyed fight after fight. Obviously every team isn't going to be perfect and may have some mix and match, but do what you can to make what you have work.
Obviously I'm not the best player, but these are just some of the things I've really noticed that people could use to maybe help them, and try to improve just like I am.