Ask curious questions to dig beneath their first answer. Once you’ve asked the question, please be quiet, listen and wait for their reply. The six sigma tool, the “5 Whys”, is useful in this context.
Famous culture expert, Dr Edgar Schein says in many of his books, “Personize it.” Find out what matters most to the person with whom you are building a relationship. It might be their family, a hobby, a skill, a cause. I struck up a relationship with an extreme introvert by finding out he was passionate about cycling.
Listen to understand, rather than listening to respond. Are you waiting for a gap in the conversation so you can jump in with your point? Or are you hearing and processing what your speaker is saying to you? One courageous team I worked in was filled with extroverts and one introvert.