If you want to improve, win games, and climb the ranked ladder here are a few suggestions.
You should find champions you like in specific roles. Then you should narrow your roles and only play those 2-3 roles in ranked.
I am in Gold (III atm) and I can only confidently play two roles in ranked: Top and Support. I will occasionally have to play an "off-role" like mid or jungle but this is typically due to someone making a request on my team in champion select. Maybe someone's champion was banned, or they don't want to lane against xxx, or there is a one trick pony that got their secondary role and requests to play their main.
I can play mid (which is sort of my third role) but when I have to play it, I just try not to fuck up. I don't try to make plays. I don't over extend. I don't roam. I just simply try to farm and not die. That's it.
If your response is that you like playing other roles and champions I would say you can do that in normals. To win games more often and improve as a player you need to get good at specific roles and specific champions. I typically practice other roles in normals along with other champions.
I would say pick 2 roles you are OK playing and then a 3rd role that you can play adequately if circumstances call for it.
Pick 2 roles you DON'T want to play in ranked and simply never play them.
Then I would pick 2-3 champions per role and ONLY play those champions in your ranked games. If you get better with a small set of champions you will win more games than having a wider champion pool.
Although I have played maybe a dozen champions this season in ranked, I now am only consistently playing 6 :
and
or
if I have to mid.
I also suggest to just avoid the bot lane in silver. The bot lane is a mess down there and players are wildly inconsistent in that Elo. I would recommend sticking to Top, Mid, or Jungle.
Don't chase kills at all and if you kill opponents you should be looking to take an objective instead of backing.
On my silver smurf I notice people will back after securing kills instead of pressing a tower or taking a dragon. Avoid doing this.
Learn to farm under tower. That means if you are pressed under tower and a minion wave is crashing into it you should be able to figure out the amount of turrets and auto-attacks need to got through so that you can last hit the champion. Typically 2 turret shots and an AA for melee and an AA turret shot and then an AA for casters. I think if you run enough AD though you may be able to avoid priming the casters on some champions.
Recognize level discrepancies. I notice that Silver players have a tendency to not respect levels of champions.
One full level between 1-7 is really noticeable in terms of damage and stats. 2 full levels between 8-14 you should respect and avoid that champion. If you are level 10 and the enemy champion that you are laning against is level 8, you could probably fight and kill that champion pretty easily regardless of their kit.
Figure out what items to build and build according to the situation.
Farming is really important. Avoid missing farm to trade. A lot of silver players will miss farm to attack and then they get behind in gold and in items against their laner. I usually don't trade much in laning unless I plan to kill my laner very soon or I am last hitting farm while also trading.
I hate to say it but don't expect much from your teammates. Just focus on what you are doing and how you can improve. While the player quality did improve in gold from silver, my teammates will sometimes make really bad mistakes.
I can't fix those mistakes for the most part, so I try to just focus on what I can do to improve.
I can't stop my adc from dying 3 times prior 7 minutes from the top lane. I can maybe TP, but my TPing to a losing lane may put me behind my laner.
When you try to band-aid losing lanes you sometimes sacrifice a lot and this can effect your level of strength in the game. It is cool trying to help a teammate, but I typically only try to help teammates when it is convenient and they demonstrate that they can catch up.