Interview using all of your senses.
When doing a face-to-face interview, don't just hear what the person is saying, 'listen' with all of your senses engaged. Look at the way their eyes light up over certain topics, the way the sunlight picks up different colours in their hair, the smell of their home or perfume, the background sounds of children, pets or music, whatever you can pick up about that person and their situation from their surroundings.
Taking in all these aspects when interviewing someone for an article (which is what makes up half of my freelance writing work) brings to life your experience of your time with that person. The reader gets a more rounded view of the interviewee, and your article is more enjoyable to read as it is richer, deeper.
This would not apply when interviewing people for short quotes or when interviewing via email. However, you can extend your listening skills when interviewing via phone to pick up when the person felt tense or excited discussing certain topics, for example. Practice when talking to your friends and family.