How To Climb Out of Bronze and Further
The best way that I found to climb out of Bronze, is to play support. I climbed from Bronze 3 into Silver 5 by playing Sona. I bought Sona because she is a universal support that goes well with any adc. Another perk to her is that she doesn't take much skill to get down to a decent level. Her heal allows for ability to stay in lane longer as well as a shield that helps in fights. Her Q (her main damage) is great for poking so when a fight does come along the enemy team is already lower health. She has a speed boost to help either run from a losing fight or run up to finish off a kill. And then her Ultimate stuns everyone in her path which allows a solid 1 1/2 seconds for you and your adc/team to lay into anyone stunned.
In my experience, and I've been playing since season 1, a really good support can win or lose a game. One thing that people forget as a support is that you are supposed to get you adc as many kills as possible. It means you do everything you can, even if you die, to keep them alive and hopefully get them some kills. I've had supports that will be 6/3 by mid game while I was sitting at 4/4. My support would get double kills in early game and i would rarely get a kill. And then my support was getting mad at me because I was playing more passive Mid/Late game because I really couldn't do a ton of damage but enough to help the team. I would've been a lot more helpful and we probably would've won the game quicker if my support had allowed me to get the kills early game.
My favorite supports (that I own) are Sona, Thresh, and Nami. Leona is also a good support that require not much skill but I do not own her. Pick a support and get good at them and I promise you, you can climb the Ranked ladder.