Get into the mentality of "Do not die" rather than "I must kill everyone for a good kda". The thing about LoL, is there is snowballing, and once the enemy gets ahead of you, they most likely will be able to kill you pretty easily. This mainly applies in lane. I hate it when people continue to try and burst a champion down, when it didn't work at level 1. Hey, they are now level 3, if it didn't work before, it won't work now with you still at level 1. Sit and wait for your opponent to give you an opening. When it happens, take it if the risk isn't huge. After all, if you are behind by a bit, you don't want to get behind by A LOT. If people start feeding the game spirals out of control and becomes more and more difficult to win. If you overextend you should make sure you can get out safely via warding or abilities.
Don't be afraid to leave your lane. LoL is primarly a team game and you should watch what is happening in other places via minimap. In my last game I left bot lane and went clear to the other side of the map to baron river to aid my team. It ended with four kills for our team and only two deaths. If I hadn't have gone, it would've been two kills and three deaths, causing our team to get further behind while I'd be farming greedily for cs.
Use pings. The smartping system is amazingly helpful and very easy to use. Use the "on my way" ping when you are on your way, and use it around the area you will appear from so your allies know that help is coming and from what direction (that is alt+left click mouse right, release click). Pinging in the middle of a fight with the "on my way" ping isn't as helpful, as allies then need to look to see what direction you are coming from. Ping for assistance when you see the enemy about to push a lane and take a tower (alt+left click, mouse down, release click). Using these will help get team members more organized. I've also seen this used when the jungler is about to fight dragon, very helpful.
Retreating is a viable option, and in some cases helps stall the snowballing. If there are three to four people in your lane verses just you, and no allies are on their way, just leave the tower to it's fate. Yes, towers are objectives and give massive gold, however, it's better for them to just have a tower rather than a tower, a kill, and three assists. My support last game left the tower when three were bottom, and I couldn't be more proud that they did that instead of giving them a free kill, assists, and a tower.
Look at your minimap. Seriously. It's not only the supports job to do this. You contribute nothing to your team if you are in a lane last hitting while a huge teamfight is going on one lane off from you. The only time you would is if you were split pushing. Don't be the guy who ignores everyone and pretends like he's playing a single player game (unless you are Nasus and haven't fallen completely behind).
Thank your jungler and support. These two jobs are primarly thankless. Thanking your jungler for ganking, or thanking your support for doing their job right goes a long way. You might be 15/0/0, but you didn't get that way with just your talents. Thanking will only help your position for a number of other reasons as well.
Realize the game is not about individual score. The goal of the game is to win, not to have the best kda. If what you do gets you killed but places your team on top, you shouldn't have a problem with that and no one else should either. If you are just plainly feeding just try hard to stop and help your team any way you can. Don't ever leave a game either. Mute abusers and communicate with pings.
Play champions you know, not what you are told or just picking it because it's top banned or top win-rate. Like all those horrible Rammus a bit ago. Ugh... -shudders-
These are just a few things that have made me a better LoL player over time. You might find them basic, but I really am amazed when people don't do some of these things. If it helps you, I'm glad. If not, sorry for wasting some of your time.