I suspect that the most basic and powerful way to connect to another person is to listen. Just listen. Perhaps the most important thing we ever give each other is our attention. And especially if it's given from the heart.
When people are talking, there's no need to do anything but receive them. Just take them in. Listen to what they're saying. Care about it. Most times caring about it is even more important than understanding it.
Most of us don't value ourselves or our love enough to know this. It has taken me along time to believe in the power of simple saying, "I'm so sorry," when someone is in pain. And meaning it.
One of my patients told me that when she tried to tell her story people often interrupted to tell her that they once had something just like that happen to them. Subtly her pain became a story about themselves. Eventually she stopped talking to most people. It was just too lonely. We connect through listening. When we interrupt what someone is saying to let them know that we understand, we move the focus of attention to ourselves. When we listen, they know we care. Many people with cancer can talk about the relief of having someone just listen.
I have even learned to respond to someone crying by just listening. In the old days I used to reach for the tissues, until I realized that passing a person a tissue may be just another way to shut them down, to take them out of their experience of sadness and grief. Now I just listen. When they have cried all they need to cry, they find me there with them.
This simple thing has not been that easy to learn. It certainly went against everything I had been taught since I was very young. I thought people listened only because they were too timid to speak or did not know the answer. A loving silence often has far more power to heal and to connect than the most well intentioned words.