or: The Five Principles that I wish I had Known in High School when I was Busy Picking Silly Debates that Got Nowhere and Accomplished Nothing and Acheived Absolutely No Clarity and were Really Just There to Keep Me from Going Out of My Mind from Boredom.
1) Shut up. No, really. Just close the mouth. That's better. No, you can't talk yet. Just hush...that's better.
You don't always have to be fighting, to be picking your next argument, to be analyzing and counteranalyzing for weaknesses and talking points. Just listen. What are they saying? No, really, explain it to me. Can you formulate their argument? Can you flowchart it? Can you chop it and dice it and toss in a couple of its implications and a handful of its premises?
Let them finish. Your question on the first sentence shouldn't be an excuse to stop listening to the rest of it. Especially when it's not really a question, but a snarky attack at some flaw in their reasoning.
2) Be clear. Focus, as Michael Medved would say, like a laser beam. You don't need to go into the whole windup, with rant and example and clever turn of phrase. If there's nothing that you disagree about enough to be able to simply swoop in on a discrepancy, then do you really disagree or are you just arguing out of principle?
Stop talking past each other, orating at each other, tripping each other into little vicious circular tangents of semantics or nitpicking. Find the core difference- the b'mai ka mafligei- and fight about that. That ought to be quite enough.
3) Boil down. Alright, you've got the actual point of disagreement. Is that based on something else? A premise you don't share? An assumption that you're not willing to make, or that you think is obvious? Almost every argument falls back to one or more other arguments. Get as far back on the Hydra's neck as you can.
Bickering about the rule about knee socks? Isn't it really a debate about the importance of mandating religious standards versus personal independence? Or maybe it's a fight about religious tolerance versus believing in only one legitimate path? Or maybe, just maybe, it's really just you not wanting to have to go buy new socks? Boil it down, redefine.
4) Pick and choose. You can't fight everything that you and your co-debater disagree about in one setting. Stick to your topic and its immediate premises. The person who supports knee-socks may also be against your learning Talmud, but you don't have to start duking out everything about every belief. If it's directly relevant, than there you are. But don't bring it in just because it's always irked you and you really want a chance to get into it. There will be other chances. There are always more chances.
5) Know when to stop. Sometimes, there's nothing left to fight about. You've boiled things down to a premise so basic, an logical jump so obvious or (for the other person) so ridiculous, a difference of opinions that are so firmly held that you're never going to get anywhere. Ever. Maybe, possibly, if the other person isn't quite as smart as you, you can trap them, puzzle them, or race beyond them, but you will never convince them.
Or maybe you've boiled your differences down to something that really isn't that big a deal at all. You would do X 49% of the time, I'd do it 50%. You are slightly less in favor of Y. I value Z a bit more than W, but they very rarely come into conflict.
It's okay to stop. I mean, yes, it means you might just have to find something else to do with the last five minute of your recess, but that's okay too. And another twelve hours of point and counterpoint, jab and foil, nitpicking and example aren't really going to do anything. You don't have to 'agree to disagree', but it's okay just to agree to stop arguing and talk about the weather.
The only other point that I would have is more a rule of morality than of debate, but I would still like to mention it, because it's important. Obvious, but important. Don't debate people that you dislike, and don't dislike the people you debate. Arguing should be a way of connection, not an excuse to vent all your dislike of an idea/principle/system/theory onto the head of the perfectly lovely person that happens to be supporting it. And if you don't like the person you're fighting, you're going to be associating their flaws to their position and vice versa, making it difficult to have a really intelligent debate and virtually impossible to ever accomplish anything in your argument