Cultivate an attitude of discovery and curiosity. Pretend you don’t know anything (you really don’t), and try to learn as much as possible about your opponent/partner and his point of view. Pretend you’re entertaining a visitor from another planet, and find out how things look on that planet, how certain events affect the other person, and what the values and priorities are there.
If your partner really was from another planet, you’d be watching his body language and listening for unspoken energy as well. Do that here. What does he really want? What is he not saying?
Let your partner talk until he is finished. Don’t interrupt except to acknowledge. Whatever you hear, don’t take it personally. It’s not really about you. Try to learn as much as you can in this phase of the conversation. You’ll get your turn, but don’t rush things.