Have you ever noticed, when people are like each other, they LIKE each other? Rapport is building that layer of responsiveness between 2 people. It doesn’t mean automatic liking, but it definitely gives you the feel of liking.
Here are some ways to make people more comfortable and to build rapport:
Notice their posture, gestures, breathing and facial expressions. Be subtle but begin doing what they are doing, perhaps adopt their posture, their gestures, angle of their head, arm positions. You can match tone of voice, volume and tempo. Notice their words, their delivery and see if you can match.
At first, just pick 1 or 2 elements and give it a go. Again, subtlety is key here, if they are throwing their arms around, perhaps pick something else. You will notice the change in how you are being received, it is truly remarkable.
Meeting people in their model of the world builds trust, lessens inherent suspicion, and our brains are wired to like people who are like ourselves!