How to I prepare for a Cambridge interview?

If you got an interview you are already halfway there - congratulations! The interviewers liked your application and think you have potential, so your job during the interview is just to try to convey that potential as well as you can. You will likely have two interviews, done by two or more different people, which test your eligiblity both for the Cambridge system - which is quite demanding - as well as for the particular course you want to take. During the interview which assesses how suited you are for the Cambridge system, the interviewer will check how well you will handle the supervision system. This system means that you will have a number of meetings with professors/lecturers/post-docs/PhD students each term, where you discuss your work, have an opportunity to ask questions and where you will be questioned. These meetings are usually either one-on-one or with no more than a total of four students, meaning you will have to participate in the discussion! The interviewer will test your suitability for this system by asking you supervision-style questions and see how you react and respond. Some things to think about during this interview are:
You won't know the answer to all questions, and the interviewer doesn't expect you to. Rather than just checking your actual knowledge they are checking how you react to not knowing the answer to a question, and how you try to approach the question. Students who give up as soon as they don't know the answer will likely not benefit from the supervision-system. If you don't know the answer to a question, you are perfectly fine to tell the interviewer that. You can perhaps say: "I'm not sure, but I would think..." and then start working your way around the question. Don't worry about making mistakes! They want to know how you think.
Supervisions are not meant to just test your knowledge and reasoning - you are not assessed on supervisions. They are there to help your learning and should be a fun opportunity to learn more, so try to approach the interview in the same way! If you don't know the answer to a question, rather than panic, try to see this as a fun opportunity to learn something new. The enthusiasm will impress the interviewer!
Finally, for the subject interview, you will be expected to have some background knowledge. You might not have studied the topic for, so your knowledge doesn't have to be in-debt, but you need to show a clear interest in the topic. You might still get questions that you don't know the answer to, but the same rule applies: try to work your way around it and show the interviewer the things you DO know! If you show that you can think on your feet and have a clear interest in the subject then you will be just fine!I studied psychology at Cambridge and here is one of the subject-questions I got: "if you wanted to create an experiement to test whether mice can tell the difference between the colors red and green, how would you go about it?" Even if psychology is not your topic, try to think to yourself about creative ways to approach this question!