The single-most important thing I learned is to realize I am not raising children, I am raising adults. By about spring of my DD's junior year, when she'd ask me if she could do something, I'd think to myself, "well, she's going to be gone in a year, so now what?" -- the goal was to get her used to that kind of freedom in a responsible way. Of course, this is the kid who has wanted to be independent since she arrived on this earth, so that was just the tail end of a long history of figuring out how much freedom she could handle.
The specific details depend on your kid. For ex., DD was the "verbal diarrhea" kid. I had to figure out that she processed her emotions verbally, that what she said often wasn't what she meant, and that in any event, it wasn't about me. That helped a lot during the frequent highly-emotional rants -- it enabled me to see the hurt underneath and respond to that rather than getting triggered by something insulting or hurtful that she said. She also saw any advice as evidence that I didn't think she was competent, so I had to learn to bite my tongue (but she was so wrong! the problem was so easy to fix!) and just say things like, "wow, that's so frustrating -- so what do you think you're going to do about it?" There were even times that I had to stretch it and act like I agreed with her about school stuff (e.g., teachers being mean), because what she really needed was to know that I had her back and had confidence in her ability to manage the situation.
DS (8th grade), OTOH, is exactly the opposite. He keeps everything inside, and he can be a sneaky SOB at times -- the phrase "smile and smile and be a villain" comes to mind, as he's cute and has definitely learned that he can get away with more simply by being nice and agreeable and then doing whatever the hell he wants when backs are turned. Luckily, he is fundamentally a good, nice kid, but he definitely stretches it and sneaks where DD was a total rule-follower (she'd scream and moan but comply; he'll say "of course" with a smile and ignore).
I'm definitely still figuring it out with him. But even though they react differently, both kids want to be seen as good kids, and they want the freedom to do what they want to do. When I caught DS out doing stuff he shouldn't have been doing, the response was grounding -- no electronics of any sort, no running around after school with his friends. Because what he was loving more than anything was the freedom to be on his own after school and go do stuff with the guys. So I explained that he gets that freedom because I trust him to make good decisions, and when his actions demonstrate that I can't trust him to do that, then he loses the freedom. And then I had to come up with things he could do to earn my trust back. We had to go through that cycle a couple of times, but we seem to have gotten through that particular issue (although I am sure there are more in our future). But I still struggle to get him to talk about the things that are bothering him -- he is a private kid and hates prying, so I let him know that I am here if and when he wants to talk about anything, but that he doesn't have to if he doesn't want to.
The thing that applies with both kids is that when they are acting like entitled twits, it means I have not asked enough of them. So when DD started being intolerably bitchy around 12.5, I explained that if she is taking things for granted, then I am clearly carrying too much of the load, and so it was now her turn to make dinner once a week. But of course the underlying issue was really that she wanted to be seen as grown-up and capable, so the more responsibilities I gave her -- and the more I worked with her calmly to teach her those skills and praised her for learning them -- the more she calmed down, because what I was really giving her was the opportunity to prove to herself how capable she actually was.
Above all, love them. When they are the most impossible is usually when they need unconditional love the most. I would remind myself that this is a really fundamentally good kid, so imagine how terrible it is to be inside their head at that moment, with so much emotion roiling around to provoke that kind of outburst/behavior.
