Stop Fighting and Start Pushing!!
If you want to climb a lot easier, you need to stop fighting and start pushing! After laning phase, you'll typically find yourself doing that 20 minute ARAM. Your goal is to prevent this ARAM for as long as possible. This ARAM is where most players lose their lead, tilt, then blame others. You need to split push and keep constant pressure on that lane. This will ensure that someone will always be in that lane to stop you from taking tower. Your splitting will pay off in the long run. You'll have a level lead, gold lead, and players are more likely to listen to you if your doing well. Just simply tell your team to play around you, and when you start joining in on those ARAMs because you'll dominate it with your lead then carry the game. Not all champions have this potential, so I highly recommend you play top lane because this lane has many champions that can 1v5. Mid doesn't work out well because everyone is there 24/7, ADC doesn't work as good because your support will typically follow you around a lot and share XP. Never stop split pushing unless you think your ready to carry a fight.

Stop Blaming Your Teammates!!
You can blame your jungle, mid, top, support, adc, it does not matter at ALL. If you can't win lane, your not gonna win games. It's alright to let the enemy take the tower first in losing matchups. The wave will push to you faster which will allow you to farm safely. It's your job to get a lead by punish your enemies mistakes, if your in silver, I doubt they will play perfectly. If your entire team is losing, you want to completely ignore them. When I say ignore them, I don't mean let the enemy team take your nexus for free. Its alright to give up a dragon or two. While the whole enemy team is all grouped up together, you'll be alone getting a lead on them. Split pushing and actually getting something is better than walking towards the dragon pit, losing it then having to walk away and get nothing. When you play, make the choice that gives you the most guaranteed instead of doing a coinflip which is all or nothing. Sure, you'll get troll teammates every once in a while but your not getting them every single game. Challenger players don't struggle at all when smurfing.
"Well of course you dweeb they're Challenger," says a random person.
Challenger players can climb easily because they never make a play that's 50/50. They will only make plays that are in their favor and they are able to take over the game because they know how to keep their lead.

Realize Your Own Mistakes
You lost, you can't change the past but you can change the future. You don't need to replay the whole match but if you want to, you can. Think about simple things you could've done better. Sure you got a good KDA but does that KDA really matter if you lost? A lot of people get hard stuck because they can't man up and admit their own mistakes to themselves. If you get a lead, you can carry the game, if you didn't carry the game, you did something wrong.

I Already Know All This Stuff
You already know all this stuff? Doesn't matter your still in silver. When you play a round of league, don't get tilted if your team gives first blood. You can completely change the fate of the game yourself. No one is controlling what you can or cannot do. Climbing out of silver doesn't need insane game knowledge or mechanics. You'll climb out of silver when you're able to recognize the correct plays and explain to yourself why the play you made was bad if you made one. Something you've probably never thought of before is make plays with the tools you have, not the tools you wish you had. You can win the trade if Leona stuns the ADC, but she doesn't go in and you die. If this happens, you can completely cut Leona out of your choice making instead of trying again then dying.