If we're talking family: I either don't argue at all (which is the preferable option I choose most), or if the issue keeps recurring and some negativity arises, I will get down to the root of it, I will get down and dirty and dig and get messy until we fix it and I'm confident that there was some growth and gained understanding from both sides during the disagreement that we can all walk away with and be less likely to run into the same bad pattern next time.

Even if that means I come back half a day later and bring it up again when we're all calmer.
I try to use kindness, and to see things how the other person sees them.
If it's strangers, or people on the internet: Very minimal arguing. I will say my point boldly, and if they disagree, I gauge how open they seem to my point of view. (I think I have gotten pretty good at being able to tell when someone is open or closed.) If they don't seem open, I won't bother and I'll just let them have the last word....though It's tough to walk away if they try and bait me with perceived false assumptions against me.
I avoid debates like a plague. They solve nothing.
I hate arguing with a passion...but I love resolving things with a passion. It's a bit of an internal conflict with me.