PSA: You're not stuck in Silver/Bronze, you just aren't playing it right!
No one is stuck in Bronze/Silver, no one. It's an illusion. If you think I'm one of those "ohmygod this guy again, says elo hell doesn't exist" look at the history of the threads I've made. In preseason and Season 5 I made NUMEROUS threads about it. I know it exists, I know people suck, but the ENTIRE issue with why you're in Bronze/Silver is YOU. Nothing else, just YOU.
Now, you all probably think I'm absolutely batshit crazy, right? I'm not. I've found the light and I found out how to climb out, and trust me, it works, even if you're the absolute worst player ever.
Okay, so if you're reading this, you're either a high elo player seeing what I have to say or a low elo player who has researched how to get out of bronze/silver. A LOT of guides recommend playing a simple champion, like Jax. This isn't 100% true, but for the most part, I recommend this. Go onto the LoL wikia, look at the champion list, sort by the champion skill, and pick one that is below a rank 6. These ones, typically, are going to be on the easier end to get the basics of and on the moderate end, at the max, to master.
Pick ONE champion, and if it's FOTM or potential FOTM, pick a new one. That means no Jax, no Udyr, none of that. Irelia is a good pick and it's what I've been using. Also the most important thing to remember with this champion is to MAKE SURE YOU ENJOY PLAYING THEM. You need to be able to play numerous games as them without getting bored, meaning don't play someone you don't enjoy playing.
Okay, I picked a champion, what now? Play AT LEAST 20 normal games as them. Make sure you know them for the most part and you know how the current common matchups go. If there's someone that you specifically hate going against, like me with Riven, try to find someone who plays them and ask them to help teach you the matchup. Chances are, they'll gain knowledge on the matchup too, so it will be good on both ends.
I'm good as this champion and I have their mechanics down and know their powerspikes! Can I do ranked now? No. Go into a custom, just yourself, no bots, aim for 70 CS by 10 mins. This will put you ahead of most Bronze/Silver players off CS alone. You get 70 CS at 10 mins? Do it again. Until you're confident in your CSing skills, do this.
Okay, I just hit 70 CS by 10 mins as my average! Can I PLEAAAAASE do ranked now?! Yes. Do ranked. You have your microplay down pat at this point, hopefully, and now you can practice what you truly need to practice in ranked, macroplay. Macroplay is basically taking objectives like turrets, dragons, baron/rift herald, TP ganks, etc. as well as team-fight and skirmishes.
You have your microplay down at this point, you shouldn't have to worry about your mechanics or how well you did in lane, because if you have the microplay down, you shouldn't die much, and if you do, it should be worth or at least an even trade. You should have plenty of CS meaning you'll have plenty of gold. You WILL have games where you're under turret constantly and get denied cs, which is fine, that happens, but overall, you should be ahead goldwise because you know how to CS better than a majority of Bronze/Silver players. If you can outplay them, go for it, especially if it's an easy matchup.
By doing this, you should be able to climb out of Bronze AND Silver within a month or two (minus the prep time of finding a champ and practicing them). I've noticed when I look at people who add me after games' match history, more often than not, they play a bunch of different champions. Sometimes they will play only 1 role, like ADC, but sometimes it's not even that good. They complain that they're still in Bronze 3 when I'm in Silver 5, then I get to Silver 1 and they're only Bronze 4. This is EXACTLY why you main a single champion.
TL;DR: To climb, main a single, non-FOTM champ that you enjoy playing. Practice CSing and Microplay, then use ranked to practice Macroplay. Only ever play the champion you main in ranked, and if you have a period where you get bored of them, go to norms to play others.
Side Notes from Comments:
- Ignore Chat. Unless it's healthy chat ("Hey, 45 seconds on dragon, let's fight then take it.") don't bother.
- You have to realize, if you're in Bronze or Silver, YOU'RE BAD. There's no easy way to say it, and there's no point sugar coating it. Following these tips will help you get better and get you out of Silver.
- There was another thread I saw a couple minutes ago, Bella Blue was the OP of it. I don't have the link, but her advice was... Don't play during summer, don't play on weekends, don't play during breaks (Christmas time, Spring Break season, etc.), don't play in the afternoon (4pm EST to 10pm PST [so 4pm-1am EST]). Best time is late at night (1-4am EST) because it's early in the night, no ones SUPER tired, but the kids are in bed for the most part.