How I escaped Bronze (and maybe you can, too)
Let me open by saying that I am not a pro at this game. I'm not even that good. I'm only Silver V, nothing special. Season 4 was my first experience with Bronze, as I had been Silver in Seasons 2 and 3 (2 without playing Ranked, only by being on a team with friends that did). At first, I had planned to play zero ranked in Season 4, and just enjoy the game. Eventually I caved in, after about six months into the season. After 4 wins in promos, I was dropped into Bronze 4, and was heavily discouraged. However, I decided to climb anyway. I don't play too much ranked, but I did slowly begin to make my way up. I managed to get to Bronze 1 with ease. After that, I climbed from 0 LP to 100 LP without losing once, and proceeded to bomb my promos and drop back down to about 40. Eventually though, I brought myself back up and today finally pulled myself back into Silver. Once I figured out the secret to Bronze, it was fairly easy. Your experience may not match mine, but here's what I noticed.
Do Not Support (Yet). Even a good support is going to struggle in Bronze. When teammates run away from you, throw themselves into the enemy team, do not pay attention to your calls, you are going to have a rough time. There is nothing wrong with support. There is everything wrong with Bronze. But you're not going to be as useful when your teammates don't know how to click a lantern. Save the supporting for Gold.
Watch your win rate. I have a 100% win rate with Singed. I average over 300 CS with him per match. He is my main and my best champion. Ever since I dropped to about 40 LP from lost promos, I started playing Singed. I went on a hot streak and blew through promos and never lost again. Find your high win rates, and stick with them.
You have to get your good role. Have a specialty, be it Jungle, ADC, Top, or Mid. When you get into the match, you say "Top Please" or "ADC Please." Maybe even tell them you have a 100% win rate with your champ. Make sure you get that role you're so good at. If you don't, you're leaving your fate up to four random dudes. And they will let you down every single time. It may not hurt to dodge.
Your kills don't mean as much as you think. You got 10 kills and 10 CS? Fine, fine. That's okay. But you know, someone with 160 CS is basically at the same gold you are. Don't worry about getting kills so much. Chasing a kill may get you killed in turn, and then you've only set yourself back. Instead, chase them away with 10% of their health and take their tower. What are they gonna do? Jump in and stop you? More like give up a tower and a kill.
If you aren't farming, you'd best be actively teamfighting. If you aren't doing either, time is wasted. CS. CS. CS. 15 CS is a kill. And 15 CS is a lot easier to catch than a LeBlanc with 40% CDR.
Only teamfight if it's good for you. If the enemy team kills you every time you group, then stop grouping. Spread out. Push lanes and back off. You're getting gold while they're running in circles mid lane (because they're Bronze players and that's what they do with their free time).
Damage the tower. Did you just kill the jungler and the bot laners? Is your jungler around? Cool, you know what to do. Take dragon, and then put some damage on the tower. Even if you don't get it destroyed, you still did something productive before recalling, and even more than just taking a dragon.
Dragons matter a lot. Get the first dragon buff and you're ready to go. Get the second and you're going to be pushing like a champ. Get the third and then you can do more stuff in less time. Get the fourth and you can get more CS, get more items, and CS harder. It pays for itself. And if you get that fifth dragon, well, you're a true American hero.
Force the enemy team to make bad decisions. Singed is especially good at this. Ghost and ult, then run through the top lane and push insanely hard while your team gets dragon. The enemy team will either definitely lose a tower, or definitely lose dragon. Plus, the odds are your team will still get dragon.
If your team listens to you, then you are blessed, my friend. If you're not good at making the decisions, then maybe skip this step. You belong in Bronze. If you are, well, then you have no reason to lose at all. Even if your team sucks, if they do what you say then you can lead them to die less, or push more, or farm, or something.
Get lucky. This is an important step that you can't guarantee. You have 2 AFKs? You're unlucky. But what can you do? Not much. The enemy team has 2 AFKs? Congrats on the easy win (or truly embarrassing defeat). Nothing can make a match easier than that (with the exception of more AFKs). No amount of advice I can give will help you to win more games than getting lucky. You may get good teammates, or bad enemies, or an enemy troll or enemy AFK. Alternatively, you may get terrible teammates, Diamond level enemies, two troll teammates, and four AFKs. It's all a matter of chance, and outside your power. I got very lucky to get passable teammates towards the end of my Bronze run. In my promos, I had an AFK player on my team 6 out of 10 matches. I was unlucky, but the bad luck went away.
With these steps, I hope more people can escape the horrors of Bronze. It's significantly less embarrassing to sit in Silver V than in Bronze IV.