What is the best way to approach an unseen piece?

Read through the whole piece, underlining anything that is immediately striking / a bit interesting, even if you don't quite know why at first. Depending on whether you've been given a prompt (i.e. discuss X in the passage below) or are just commenting generally, this first read-through is essential. The bits that you know are "interesting" but can't quite decide why at first are often the bits that will get you most credit for commenting on, the bits that need unpicking. After this initial read through, make a quick note of the theme of the piece, what's actually happening, so you have a grasp of the whole.
Whatever the assessment, it can help to go through systematically and tick off structural points so you have something to talk about. Who is speaking? What is the form? The genre? See if you can note any poetic or rhetorical techniques: alliteration, assonance, metaphors, similes, personification, enjambment, caesura.... When identifying these poetic techniques for response to an ELAT, an exam question, or an interview, it is sadly never enough just to state their existence. They're either there because they're purposely inserted by the author and therefore MUST be commented upon OR they're an accident, and might as well be ignored. You will never have to talk about everything but a good range of these kinds of things, and an attention to detail within them, demonstrates the ability to close-read well. Once you've made your observations and thought about some of the effects of these devices, you can plan a response: an introduction which demonstrates your awareness of the piece as a whole, plus around three planned paragraphs of three themes each, and a conclusion in which you advance something new is often a good way to go.