The secret to climbing:

Play support.

Looking through my history (like, way back), I've noticed that my best games are when I either queue as support, or have a good support friend I queued with. So, I wondered why that is, since I can play any carry role and get stupidly fed, but still end up losing. I think I've found the answer now, though!

See, a lot of people think the support is just the babysitter for the ADC, and some supplemental damage / CC later on in the game. For a long time I thought that too. But, now, I'm realizing that support could easily be one of the most influential roles in the game, and can determine whether you win or lose.

The support is the one person who doesn't worry about getting kills and getting fed on the team. Instead, they're there to make sure that their team survives every fight and teamfight, and to prevent their carries from carrying.

Solo queuing as carry roles, I can get extremely fed, but still end up losing mid-late game. I was doing fine, so I thought I should win, right? I always complain about not having a team I can rely on, but they did always try, so why did I always lose? It wasn't because I was just bad (though that could be a part of it), but, rather, it's because my support wasn't working to prevent their carries from stopping me. That's why I have such a high winrate when I queue with my brother (a support main), because I know I can rely on him to control teamfights, and keep their carries down while I do the damage.

So, yeah, it might not be as much fun to play someone like Leona and just stun people while others get all the kills. But, even if it doesn't feel like it, the reason you won that teamfight is because you kept control of the enemy team, and prevented their carries from dealing damage and stopping your carries.

Support is a lot more than just the ADC's babysitter; a good one can win you the game, while a bad one can make you lose when mid game rolls around. So hey, be nice to your support, maybe they'll carry you. :P