I've engaged in discussions of various topics over the years and developed a few guidelines and practices which I try to adhere to. Starting with the "training-wheel" arguments typical of high-school and college age, and evolving through many of technology's "religious wars" (vi vs. emacs, Microsoft vs. Linux, etc. -- particularly the latter).
Among them:
• Go Socratic. Sometimes the best way to convince someone is to let them argue their own way out of their position. Ask questions rather than make assertions or pound facts.
• Realize that often the game isn't to convince. I have positions I hold strongly, most on the basis of experience, evidence, or logic that's convincing to me (and I'm occasionally persuaded to change my mind). But in discussing them with others my objective is often to understand what the basis of their position is. I might learn something. Fairly often, I'll find that the views aren't well-founded or aren't convincing (strengthening my own conclusions).
• Distressingly often your'll find that a person's primary argument is "it benefits me to claim this belief despite no rational or factual basis for it" -- it's Upton Sinclair (and Al Gore)'s observation: "It's difficult to get a man to understand something if his salary depends upon his not understanding it."
• Rejection of concepts is often driven by fear. I ran across this passage re-reading Robert Pirsig's Zen and the Art of Motorcycle Maintenance: "You are never dedicated to something you have complete confidence in. No one is fanatically shouting that the sun is going to rise tomorrow. They know it's going to rise tomorrow. When people are fanatically dedicated to political or religious faiths or any other kinds of dogmas or goals, it's always because these dogmas or goals are in doubt."
• Psychology is a hell of a drug. There area all sorts of weird aversions people have. I've met pathological liars. I've met people who simply deny obvious truths. Who feel "it's not a lie if I simply don't say it" (the lie of omission) or "if I only try to draw your attention from it" (lie of distraction). People are rather less rational than you might hope.
And for all of that, I've had some pretty amazing, interesting, and productive exchanges, often in the oddest places. Pulled into a highway rest area in the deep south a few years back, started talking with another man there. We both verbally circled for a few minutes trying to suss each other out, then realize that, actually, our views were fairly similar despite the miles that separated us. That was one of the more interesting 45 minute conversations I've had in years. Possibly decades.