It's not a skill that often gets taught in school...
But it should be. More specifically, critical thinking skills should be taught. The focus should be on teaching kids how to think rather than what to think. If you have good critical thinking skills, how to make a proper argument should follow. From my experience, 'debate' classes are often horrible flawed in that they use a structure which forces you on side or the other then tells you do defend that. But that's not what debating should be about. That promotes an environment were participants don't want to admit when they are wrong and were they will avoid areas that make their our arguments look weak. If your goal is to arrive at an understanding of the truth of the matter (which it should be), then you need to be willing to following the reasoning wherever it goes and not be afraid of being shown to be wrong. If you are wrong, then change your position. There is nothing wrong with that, but it usually won't happen in formal "debate".
A couple of dishonest tactics I've seen often used in live debate (meaning such as face to face, where time is an issue so a response must come quickly.) One is called the Gish Gallop. This is where the person throws out claims one after another, most of which containing lies or half-truths, strawmen, or other logical fallacies. The idea is that it takes only a few minutes to throw out all these claims, whereas it takes far far longer to deconstruct it to point out all the problems. And thus to the general public the other person appears to be unable to refute the claims, when really it's only because of the time constraints.
Another is to assert something with such force and confidence that it throws the other person off guard. Often this claim will be something so absurd that it warrants ridicule. But since the person is making the claim with such force, it can be extremely difficult (or maybe even impossible) to refute it without coming off as offensive. It's essentially hiding behind the need to remain civil and respectful. And usually involves confusing attacking the argument with attacking the person making the argument.
Honestly, anyone using these sort of tactics has already lost. They are admitting that they can't actually defend their position. Unfortunately, the general public often can not recognize this and might even claim that this person "won" the debate. It's kind of sad really.