Kiwi - League of Legends

Normally when you play LoL you don't really think on what to do, everything is pretty much automatic, last hit, harass, kill enemies, get towers, gank, control dragon, baron, teamfight and win, it's so automatic that getting out of that is what makes good players good.
HotshotGG said once something like "Every second you are not getting gold and/or experience you are wasting time", that really helped me be more useful to my team, get out of the automatic mode, and think what's better to do.

If you are a carry (not jungler or support) you must be always looking to farm, spend the most time possible farming, this doesn't mean to not b for a long time and get killed for that, but, everytime you b, check where you can go to farm, and when your lane partner is mia, of course you should say it but consider farm the time he spends away, this can give you some gold and level advantage, which will be really hard for your partner to fight against.
Say you are solo top, your enemy is mia, you suspect he will be ganking mid, you ping and warn your mid partner and keep farming, he fails his gank, and comes back top, by the time he comes back, you are already 15 cs ahead of him, that's like 300 gold, it's as if you killed him! He also lost experience. Sometimes though you have to follow him, it depends on the situation, but the point is, do something productive, if you gank and fail, you wasted time, gold, and experience.

Another important thing is knowing when to push, say you are solo top, and there are 4 bottom, the tower is at 1/4 hp and probably going down, it's surprising how many people try to go help in an already lost tower, what you should do is keep pushing, and try to get the tower, so it's one for one, or sometimes even better! Split pushing is really useful, but you have to know when to do it! When there are two missing it's normally a very nice time, if there are more only do it if you know you can escape, if you are someone like Shaco you are probably gonna be ok, or if you have teleport. Again, the point here is do something with your time.

Anyways, it's not always farming, once you have an advantage, you have to know how to use it, there comes a time when you teamfight, and you can't always leave your team 4v5, that's where experience is useful, you will know when to fight and when to push.

Another very common mistake is not knowing what to do when the enemy has baron, when they have baron you don't want to fight, your best shot is split push, push all the lanes the best you can and just defend, and don't get caught, getting caught cost games, specially if you are a carry, like Annie.

The idea overall is rather easy, just think "I don't have to waste any time, I have to always be doing something".

Again, this doesn't mean to farm top for 40 minutes, there are times when it's a good idea to gank, and you'll want to help your team with dragon sometimes, but this is experience, experience to know what to do and not waste time, if your enemy wastes too much time and you dont, you'll end up two levels ahead of him.

What you have to avoid, is beeing on auto-pilot mode, just not thinking, just farming and doing nothing else, see the map, see pushing oportunities, communicate with your team, suggest someone to push, this will really help you get some more Elo.