Developing rapport with a suspect is key to any interrogation. The reason for this is that suspects will be much more likely to talk freely if they feel at ease with the person who is interviewing them. The best way to build rapport is to do just what you would do in more social situations. That is, try to put the suspect at ease with small talk and non-threatening questions that can get them used to talking to you.
In the context of an interrogation, it is probably best to start with questions. If you try to do something like talking about sports right off, it might put the suspect on his guard. Therefore, it is a good idea to start out asking questions. Confirm the suspect’s name and address. Ask about his work and his family. But as you do so, you need to look for points at which you can interject more personal questions in a natural way. Ask the suspect what they do at work. Ask them how long they have been married or how they met their spouse. If you can make these questions flow naturally from the more formal question, you will have a better chance to build rapport with the suspect without them realizing that that is what you are doing.