I've never analysed a piece of music before. How should I approach an analysis in the interview?

Firstly, don't be intimidated by this! It's very important in Oxbridge interviews to show that you can take things in your stride even if they're unfamiliar territory. Also, remember that most music applicants will be in the same position as you, since music analysis isn't really covered in any of the A-level syllabi.
Before the interview, you will get 20-30 minutes to prepare a short analysis. Most often, it's something like a short piano piece or a Lied (German art song, voice with piano accompaniment). The first thing you should do when you see the piece is to look at the piece as a whole. Try to get a birds-eye view of the piece by asking questions like 'what is the form and structure?' and 'what mood(s) does it try to evoke and how does it achieve this?'. This helps you to work out what's most important in the piece. Then, zoom in on the things that the composer does to communicate these things to the listener. It would be useful for you to practise this method with some example pieces: have a look through Schubert's Winterreise, or Chopin's Preludes.