Relate to the person who you are trying to convince. Let them know you're in the same tribe as them. Find common ground. Be friendly.
Don't push your facts as the ultimate truth, and other facts as wrong. There are many facts that contradict each other. Be ready to agree with them, or admit you are wrong about something, as it shows a willingness to learn and grow, which is what you hope to bring out of them.
Try not to trigger a fight or flight response in the other person while talking to them, as it causes their emotions to get in the way, and may cause them to fight harder for their per-existing belief.
Try to learn something from your encounter, so your goal is not to convince the other that they are wrong, rather that you are sharing your understanding, and trying to learn from them.
