the answer is simple, it just sucks. I'll start with the inverse. Not, how do you climb, but what prevents you from climbing. To that end, here's what you eliminate if you want to climb:
*Variables
You do not want to be in a situation where you're experiencing things for the first time. This means you should be on a champion you're intimately familiar with in a role you play very often. This is best achieved by playing one role 90% of the time, with a rotation of 3 to 4 champions.
*Raging
If you rage, it's not that you're just violating the rules. You're tilting yourself. The second dick comment from a player gets them muted. The longer you wait, the less of a chance you're going to win.
*Carrying
In a perfect world, we'd play champs we like. Climbing in ranked means you have to take a champ that can carry. Look up the data on champion.gg, see who's got a high success rate in that role, see who's capable of carrying. Choose masteries and runes for those champs to make carrying most optimal.
The point is, if you want to climb, you need to mentally prepare. It isn't about skill, it's about two things:
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Tactics. If A, then B style tactics. Every Ace you push a tower. Every pushback from the enemy you should be looking at other lanes and search for rotations to other lanes.
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Think communally. Once everyone's picked, throw out a "reminder: check those summoners/runes/masteries." The question isn't about "why do I have to" it's about "i'm not blowing a 45 minute time frame because Larry took Master Yi without smite." it's about v-pinging when someone's about to chase into the jungle.
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Only Ranked when you're on your A game. This is one I screw up a lot. You should default to Normals. Get in that habit. Ranked has to be 100% concious, you need to know champ match ups, counter picks, you need to make sure you're not tired/inebriated.
The problem with Bronze is two fold: there's no bottom. Meaning you can lose 40 games in a row and play Ranked Bronze 5 for your 41st game. Making it so much harder to escape from; And people there are creating a self-fulfilling prophecy. I know folks who've made second accounts and that was the only way they got out of bronze.
When someone is screaming about how every Rengar feeds, or that Vayne's are so toxic, you need to mute, keep calm, and carry hard. And whether you like it or not you can't do that with every champ all the time. There's some modification if you LOVE a champ and have a level 7 mastery rating, but below 7, you should be taking meta-approved game savers every game all game.