Start playing ranked when you are willing to accept you're terrible at the game. This is the only prerequisite imo, because who honestly is going to care about your rank unless you're challenger? The people on the boards? If they call you some bronze scrub, they're an asshole and you shouldn't care what they say because they're probably silver, it's like someone who got 60% on a test laughing at someone who got a 59%, it's stupid.
You may be afraid to get that 59%, sure, but this isn't Korea where your future is on the line, there are going to be way more tests that you can take to raise your grade, you'll just have to study by playing and maybe looking at your own game play a bit or doing a bit of research. Focus on your own play, figure out what you need to work on, and work at improving those things.
If you're really worried about falling into bronze, focus on your fundamentals such as last hitting, map awareness, objectives, damage foresight (how much damage you can deal to kill someone and how much damage people can deal to you before you die), etc. So long as you have a firm grasp of the fundamentals (you don't need to be godly at them though), you'll be at least silver. Most bronze players from what I can tell either don't understand the fundamentals or they simply haven't played enough games to get out of bronze (10 games is a small sample size to place someone from, even if you place low or high, it doesn't matter until you've played way more games).
