Contact everyone you want to interview in advance. Don't wait until the last minute to contact potential interviewees. Give people as much notice as possible about your project and your desire to interview them. You are less likely to be turned down if you work to accomodate their schedule.
Research your interviewees. Know their background and their area of expertise. If you are going to interview a professor, read a few of his or her publications. If you are going to interview an artist, look at examples of his or her work.
Conduct a short "pre-interview" on the phone or in person. During the pre-interview, you can test out some of the questions you are planning to ask and learn more about your interviewee.
After the pre-interview, you should have a good sense about what questions will elicit the best responses. Refine these questions and write them down. It's okay to have moments of spontaneity, but never attempt to improvise an entire interview!
Although it can feel like a nuisance, collecting release forms can save you a future of headache. Make sure you get release forms for any person whose voice or image you feature and any location that is privately owned.