Talking with people that do not agree with you as though they were people. That is taking what they say seriously and trying to understand why they are saying what they say. Asking questions helps. Also, assume that they have reasons that seem rational to them for what they say or do, even if you disagree.

I think this is a very important point. If we can avoid seeing our political enemies as evil mutants, then hopefully we can avoid seeing our conversational opponents as irrational mutants. Even after discounting the possibility that you, personally, might be mistaken in your beliefs or reasoning, don't assume that your opponent is hopelessly irrational. If you find yourself thinking, "How on earth can this person be so wrong!", then change that exclamation mark into a question mark and actually try to answer that question.

If the most likely failure mode in your opponent's thoughts can be traced back to a simple missing fact or one of the more tame biases, then supply the fact or explain the bias, and you might be able to make some headway.

If you trace the fault back to a fundamental belief - by which I mean one that can't be changed over the course of the conversation - then bring the conversation to that level as quickly as possible, point out the true level of your disagreement, and say something to the effect of, "Okay, I see your point, and I understand your reasoning, but I'm afraid we disagree fundamentally on the existence of God / the likelihood of the Singularity / the many-worlds interpretation of quantum mechanics / your support for the Parramatta Eels[1]. If you want to talk about that, I'm totally up for that, but there's no point discussing religion / cryonics / wavefunction collapse / high tackles until we've settled that high-level point."

There are a lot of very clever and otherwise quite rational people out there who have a few... unusual views on certain topics, and discounting them out of hand is cutting yourself off from their wisdom and experience, and denying them the chance to learn from you.

[1] Football isn't a religion. It's much more important than that.