Just don't be one of those people who spam "tryhard" and "camp more" every time the enemy does something successful. That won't get you anywhere, except into the "people with nothing to say but tales of ignorance" category of players I shun.
Players inevitably do "try harder" in some way or another (remember when that was a go- oh wait, it's still a good thing) when they're playing ranked. You've just gotta get used to that psychology. Are they dodging harder? You'll have to be more conservative with your attacks. Know when you can get away with attacks FOR CERTAIN, not just when you MIGHT get away with them, as is usually all that matters for fun in normals. Players warding more religiously? Know this, and don't rely on the jungler to compensate for your lane mistakes. If you screw up, and the enemy snowballs, it's on you. Also know when to think outside the box. Laning against a total hard counter and don't have a shot, and you know mid will do better in your lane? Switch lanes. Tell people you're switching, but don't wait for permission. If you know it's good, do it. Not everyone who feels the need to declare their opinions in a match is going to be right. And maybe you'll make bad calls too, but let's be honest, most people you talk to in matches won't be making good calls either.
I say this from experience, but not as a high-ranked player (only silver here). I don't care enough to climb ranks. People see "ranked play" as one more justification for toxic behavior, and I'd rather climb the ranks of maturity then the ranks Riot gives me. There are times I've gotten fed up at hearing people whine at each other, and, for a few days, instantly mute all players at the start of matches. I've noticed the times I do this, that my win-rates tend to increase, my slip-ups in game decreases, and my kda's are generally better. If I ever get a solid internet service, I might start to play ranked regularly with what I've learned from this. Silence is golden. "But you can't do dat! Chat is for teamwork!" ... riiiiight, suuuure. Tell me more about this logical world that never existed...
... My point is, don't let RANKED and the mindset of other ranked players get to you as much as it does some players. Thinking "competitively" for many people degrades into thinking like a child. That "trashtalk, ignore advice, and blame 'elo-hell'" mindset won't help you as a person (I mean, sure, it'll help your self-esteem... generally when you don't deserve any) and it STILL won't help you as a player either. Put your mind into competitive play if you care, but don't put TOO much of your mind into it. Diminishing returns and escalating losses for some people. "Slow is smooth and smooth is fast". You'll do better and play better if you keep calm and chive on (yes, I said it.)
That's the end of the thoughts that come to me regarding "how to rank".