How do I answer an ELAT question?

The ELAT, although very different from the A-level format should be seen as an exciting challenge rather than a scary task - it gives you lots of freedom to be creative, and as no one has seen the passages before everyone is on equal footing. That being said, your skills of analysis, argument, close reading and presentation learnt from A level AOs or Pre U objectives can and should be transferred to the ELAT. Since the questions are often general, inviting you to “explore two or three of the following passages any ways you find interesting, paying particular attention to language, form, and structure,” there is really no set way of answering the questions, nor a mark scheme tick list. However, there are a few important concepts to keep in mind.
Initially, you should try to skim read all the passages to get a feel for the texts and the overarching theme of the paper. However, as the exam is only 1-hour long, relying on your literary instincts will be key in selecting the passages. Make sure you choose the passages which are most interesting and engaging to you (as this will come across in your answer too!) Although, not a hard and fast rule choosing two passages to sharply compare will often result in a tighter essay than attempting to draw three passages together. Make sure to write a brief introduction too, it is important to show the examiners that you are aware of what is simply going on in each text, and that the form of the passages (a news broadcast or political essay for example) are clearly identified. Establishing this strong foundation will allow you to build nuance later on into your argument. 
Argument is key too! Make sure you have one; identify it in your introduction and signpost it using topic sentences at the start of your paragraph. The examiners will be looking for candidates who can show constructed thoughts about literature, not just shopping lists; having an argument will prove you can do this! Remember too, not only to draw the passages together through similarities, but also to weigh up their differences in addressing the respective themes.
It is also very important to address the forms of the passages. Although the primary skill in A- Levels is language analysis, the ELAT requires a more sophisticated understanding of the interplay between form and content. For example, in my ELAT which I took to get into Oxford, it was essential to addresses the different ways in which a play and a poem addressed the topic of food, this fundamental contrast opened up a nuanced argument which used language as supporting evidence. As the papers offer so many options you will be able to choose a form with which you are comfortable writing on – for me this was drama. Evaluating your skills and close-reading strengths before the exam will help you feel more assured in making your text-choice.
The ELAT is all about what is written in front of you – even if it feels a bit alien (the paper could feature Middle English) no knowledge of context or critics is necessary. The exam focuses on your own skills of literary analysis and creative flair; something which you will innately have, and which can be improved through doing some practice papers. Given the time pressure of the exam expressing yourself clearly and succinctly is important, and an invaluable skill for the interviews! You therefore need to be selective with material, choosing the best points to make, and the best points at which to make them. 
Hopefully I can help you see that the exam (forgetting that fact that it is an exam) is also an exciting creative opportunity. This passion and enthusiasm will be translated in your answers to the examiners; and this is exactly the types of students that Oxford and Cambridge are looking for!