My initial climb out of silver took me maybe like 500 total ranked games. Your amount of played games will vary, but if you want to climb, you should focus on trying to maintain a 3.0 KDA with a 60% kill participation rate each game.
From a high level, if you hit those numbers, generally you did your part to help your team win. If you are able to hit those numbers and secure objectives, have high farm, or are high up on the DPS or vision score, then you are legit carrying your games.
If you are unsure of where to start improving, check out youtube. Guys like Phy, Foxdrop, are Virkayu are all good starts. I also like the Strategy Professor and Nasteey as well (but they are slightly more support focused). LoL Class is phenomenal - a little dated, but those lessons still apply.
Getting out of Silver, or any division really, requires study and change. Learn what you can, let go of your ego, and analyze your games to see what you could have done better - it's a lot harder than it sounds. I still struggle with it even after playing this goddamn game for 5 years.
Good luck to you.