Preparation, Patience, Persistence
It's not always possible, but preparing for the interview as much as you can makes a huge difference in how you come across to the person you are interviewing. With a suspect, for sure, you want to at least know the following: criminal past, household situation, recent crimes or events (break-up with girlfriend, lost job, etc). In short, background the suspect as deeply as you can. You want to know not just where he lives, but where he used to live, what his favorite hangout spot is, if he likes sports, if he is religious, and so on. Why? For one thing, it gives you more to talk about and provides a nice way to slide into normal, non-confrontational conversation in the beginning.
Patience is something very hard to teach, but it can be practiced and learned. Sometimes a good, thorough interview can take a long time. If you can't go longer than a couple of hours with someone (especially someone who has their defenses ready and doesn't want to give it up), you might consider assigning the interview to another squad member, someone with more staying power. An interview should last until the confession is obtained or the suspect says, "I don't want to talk to you anymore-let me go." Successful interviews in homicide cases have been known to go over 12 hours. Yes, it can be exhausting, but when you get that confession, you won't feel the exhaustion until later.
Persistence is related to patience. In a fact finding (witness) mission, ask the question a few different ways. With the subject of your crime, don't stop telling the subject why you know she is the one. Keep working on her, kind of like waves that keep hitting rocks and slowly eroding them.
Both patience and persistence are related to preparation. The better prepared you are, the more patient and persistent you are likely to be. If you're going in cold with little or no information on the person you are dealing with, there's not much you can do about someone who sits there shaking his head, saying, "It ain't me."