Become Genuinely Interested in Other People
It has been said that Tyrion Lannister's success in "Game of Thrones" can be attributed to his frequent asking of a simple question: "What do you want?" At a basic level, this question can help you find areas of common interest that can be used to arouse others to act.
However, the question goes beyond that superficial level. In How to Win Friends and Influence People, Dale Carnegie's fourth point is to become genuinely interested in other people. The reason is simple: most of us are primarily interested in ourselves. But as Carnegie points out, "you can make more friends in two months by becoming genuinely interested in other people than you can in two years by trying to get other people interested in you."
There are many ways we can show our interest. In Pre-suasion, Dr. Robert Cialdini cites the power of a meaningful and unexpected gift, particularly one customized to the needs of the recipient. For example, you could be in a conversation with someone and learn that they are facing a challenge, and you recently read a good book about dealing with that type of challenge. It would be entirely common to mention that book during the conversation. It would be meaningful, unexpected, and customized if you were to order the book and have it sent to them immediately after the conversation.
We are often so caught up in our own thoughts or what we want to say that it can be difficult to arouse that interest in the other person. I have heard many people say they make it their objective to learn something about the other person that they didn't know in any conversation. This, in a way, is the reverse of arousing the interest in others by asking them - it is arousing the interest within yourself in order to ask them.
At any rate, it all begins with asking questions. In the Dale Carnegie course I attended, they constructed a story to help us remember the types of questions we could ask when first meeting someone: name, where they are from/live, family, work, travel, and recreation. If you feel more adventurous, you can try to work in the 36 questions that have been said to cause people to fall in love.
There is bound to be something interesting about anyone you meet. If you consciously look for it, you will have plenty of interesting conversations, and more than likely make good friends along the way.