Some great advice from Mila Jaroniec on ThoughtCatalog. Her top two tips:
Remain calm.Appeal to science as often as possible.
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.
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.
However, I would add that if you are male and arguing with your girlfriend/wife, I'd ignore the second tip. Speaking from experience here....