Relax and listen. Guide the interview with your choice of questions, not interruptions during the answers. Take notes and ask follow-up questions. Don't be afraid to stray from your list of topics and questions. Be encouraging and considerate.
Interviews sometimes touch on sensitive or painful subjects.
Give your narrator the chance to drop an uncomfortable subject or to gather himself or herself in silence for a few moments. Let the tape run. The silences can be meaningful, too. Don't be too timid. You can ask difficult questions if you have a good reason, just ask politely.