Be in the moment with the person you are talking to, don't think about how you appear or how they are thinking of you.
Pour your attention into the other person. Observe them with tenderness and curiosity. Ask gentle open questions, not too many, just a few and let them lead you. Don't comment on much that they say - just listen, allow short silences to occur, constantly relax into their presence and refocus yourself on them. Try to find out what the most important things in the world are to them.
Most people have never had anyone really care to get to know them. To really listen to them, and accept them as they are without judgement or plans to "improve" them. Be that person for someone else and even if they never see you again, they will never forget you.
"We think sometimes that poverty is only being hungry, naked and homeless. The poverty of being unwanted, unloved and uncared for is the greatest poverty." Mother Theresa wasn't great in certain things but this quote of hers is true. Many, many people, including those of great wealth, have spent their lives feeling this kind of poverty.