Oh, I love debating! The mental stimulation it usually brings excites me beyond belief. I wouldn't say I'm especially good at arguing, but I'll see if I can help...
Whenever I get into a debate I like to keep things as impersonal as possible. The most important thing when debating - more so than winning in my opinion - is to control yourself and hold all of your arguments and your presentation to the highest level of integrity. The more composed you are, the clearer your arguments will inevitably come across and your opponent will understand your position better regardless of whether they still agree with it or not.
Be right. I cannot stress this one enough. If you find yourself to be wrong in a debate, don't roll back and don't try and sneak the point past anyway. Concede that the element of your argument in question was invalid or outright incorrect. Not only will this actually move the debate to a more productive place where people are starting to understand things, but if you're on the correct side of things it makes it very easy for you to make valid arguments and harder for your opponent to refute you.
By extension, know exactly what you're talking about before you dive into an argument. If you already have a fair understanding of the debate, you'll always be in a secure place when you're challenged. Research whatever topic you're debating thoroughly; look into the different sides and understand the basic arguments. Have your position in mind, but keep it open for change because you might just find something which convinces you that your original position may have been at least partially misinformed. Ask other people what they think about a subject, they can help you fill in the parts you don't already get. In doing this you'll understand what sort of counter arguments you're likely to face and what you'll have to compensate for.
Don't pick at the superficial flaws of your opponents argument... Well, pick at them by all means, but focus more on the fundamental problems that make up the substance of the argument. Separate the different aspects of your opponents position and find the flaws in it. Separating different key ideas makes it much easier to see exactly where they're going wrong, making your counterpoints more direct and stronger as a result. Keep an eye out for opportunities to make your opponents sound completely ridiculous by taking assumptions made by their argument and applying it to similar circumstances.
While we're talking about assumptions, call your opponent out on any that they have made without decent evidence. Some of their assumptions may not be obvious, but they're usually there. if you can identify and expose them, you can usually blow up your opponents argument right in their face, at least temporarily, as at least one of their points will usually only apply with their assumptions in mind.
In addition, when you deconstruct your opponents argument, keep an eye out for evasive language. Never let anyone weasel out of a point, make them back up their point until the element which isn't quite up to snuff reveals itself. This is really important if someones point hinges on a fallacy or something simply disgusting.
This one is more of a personal taste than anything else, but please don't bother with rhetoric. Just be clear and concise. If your points are convincing enough, they will support themselves. Emotive language, rhetorical questions, all the stuff you were taught in English, I find to be pretty worthless to the argument at best and to have an outright predatory and discouraging tone at worst.
Just FYI, if you play a drinking game where you take a shot every time the word opponent is used and you may get alcohol poisoning. Take a shot every time I say argument and you WILL die from it.
Disappointed that I forgot the biggest tip of all: If people confuse you with facts and logic, shout louder!