How do I begin to answer a question on a piece of 'unseen' poetry or prose?

Don't be daunted. Unseen questions are there to test your close-reading rather than memory skills. This can be scary but it is also reassuring as you have everything you need in front of you to answer the question, and it is something that can be learnt. Like lots of close-reading questions, students often panic and try to include everything in the passage. Remember you're not being tested on how much you can cram in. You are often given a bit of context, i.e. date published, where it was set etc. but this doesn't mean the examiner wants you to read too much into it (speak at length about the relevance of the date and so on). It is just there to make sure you don't go hurtling off in the completely wrong direction. Really read the question - highlight the key things if you find that helpful - and then read the passage with this in mind. A lot of people stress about getting all the right terminology in and end up writing an answer that doesn't sparkle in any way. It won't have a very sophisticated argument because it is structured around buzz words like litotes, syntax and so on. Let the question guide your reading and then you're in a position to formulate a clear but nuanced argument.