Discuss the ground rules beforehand. One of the greatest sources of subject anxiety is the uncertainty about the interview's subject matter. Unless you truly plan on surprising the subject, there is no benefit in this uncertainty. Have a detailed discussion days before the interview about your documentary's topic, its broad goals and the areas you are interested in discussing in the interview. Freed of this anxiety about potential "gotcha" questions, your subject will be much more relaxed, natural and forthcoming.
Plan your interview questions. A good interview is like good jazz. Before too long you will definitely be improvising, elaborating on great answers and eschewing redundant questions. However, the best improvisation is done from a solid game plan. Determine your essential, must-ask questions and then build around those. A good rule of thumb is to start with "softballs" -- easy-to-answer questions -- and slowly build to the more challenging ones.
Make the atmosphere non-technical. Lights, camera, microphones and other equipment are essential for documentary interviews. Make these technical details a secondary matter to the subject and not the focus. The essential task is the discussion between the interviewer -- you -- and the subject.
Roll camera early and start the discussion casually. Unless you are shooting 16mm or 35mm film, footage length is a minor obstacle to your production. Start the camera rolling early and mention it, but minimize its importance. De-emphasize the formal sense of an interview beginning. Your interview should be as much like a frank, personal conversation as possible.
Be conversational. Unless you have chosen a particularly formal style, you will be best-served with interview subjects in a relaxed, conversational mood. Treat your interview as an in-depth conversation, in which you are merely a friend who is deeply interested in the topic at hand. The more the subject engages with you and speaks as if to a real person, rather than presenting information in a guarded way, the more compelling your interview footage will be.
Ask open-ended questions. The worst possible question is one the subject can answer with a simple "yes" or "no." Instead of "Are you glad you joined the Marines?" try, "How do you feel about your decision to enlist?"
Follow up if necessary. Very often you will edit your interview footage and realize the perfect question you forgot to ask. Do not hesitate to ask your subject for a follow-up interview. The setting, lighting and clothing may be different, but if the information is compelling enough the audience will pay these details little mind.