Imagine this: as your opponent’s blood pressure gets higher and higher and they start waving their arms around like a red-faced loon, there you sit, calmly, evenly, acknowledging them with a steely gaze. There’s no way for their emotions to go but up, but you, master of disguise, are cool as a cucumber — even though you may be positively boiling on the inside. When every overblown accusation is met with a cool, calculated response, your opponent has no choice but to feel either tongue-tied or crazy. Either way, this is a win for you. One cannot reason with crazy.
Appeal to science as often as possible.
There is only so much people can do about facts. If you have to have a list of references at hand (hell, even Wikipedia counts sometimes) which you mercilessly lob at your opponent to stun and kill their argument, so be it. Nothing is off-limits. If they even attempt to respond to a claim you make with “And where did you get that?” you simply toss your list of references at them like a fluffy towel and watch them stammer and try to collect themselves. Of course, this means you must have a ready and working list of references for commonly-argued-about things at all times, but that’s a small price to pay for being right.
Leave the emotions out of it.
Too often, people will make emotional arguments while trying to get you to see their side of things. But this is to be avoided, as only weak-willed earthlings make emotional arguments. Keep in mind, though, that stating your emotions and the consequences of them can be a pretty powerful move, but emotions alone won’t do the trick. Instead, treat the person you’re arguing with like a room of first-graders: do not assume that they are able to feel what you feel and have the capacity to understand it (hint: they don’t), so spell it out for them clearly and slowly, possibly with a chart.
Speaking of emotional arguments, the easiest trap to fall into is the “always” or “never” trap, as in, “You ALWAYS do x” and “You NEVER do y.” If you’ve ever taken a symbolic logic class, you’ll know that this is never a good argument unless the person does, in fact, always do x or y, which is rarely the case. As a result, you must always make the effort to be 100% accurate, because any sort of floundering in logic can and will be used against you.
Know your root.
Heated arguments often tend to spiral out of control. What starts out as you always leaving the toilet seat up, or whatever small grievance, can easily turn into you being an inconsiderate mate 80% of the time, and eventually to you being a general sociopath. Watch out for this. When people argue, they often make connections between points in the argument and random things that have completely nothing to do with it. Usually, calmly saying “You’re not making any sense, talk to me when you are” and walking away is enough to extinguish the flare. However, it has also been known to further incite the attacker and result in a butcher block with the knives still in it to be thrown at your head. Use good judgment.