How do I approach writing an essay for the ELAT?

The ELAT is all about close language analysis; it is a test designed to highlight your ability to look at unseen passages. Fortunately, you have no contextual preparation to do for this exam, and it is arguably better if you do not recognise the extracts, as it avoids getting tied to extratextual details. The most important thing to remember here is to stay as close as possible to the texts.
First of all, I would suggest briefly reading each passage. You may think this is a waste of time, but in fact it is extremely important to pick extracts that work well together in order to write a successful comparative essay, no matter how interesting they both are individually. Look for similarities and differences- comparison encapsulates both of these. You may, indeed, decide to write an essay on a common theme across two passages, or perhaps on how two writers deal with the same theme in different ways. The ELAT gives you a huge amount of freedom in how you decide to structure your answer. Once you have chosen your passages, read them both carefully. Then, read them again, but this time with a highlighter and pen in hand, annotating anything that jumps out at you. Through this process, there are several pointers that you should be looking out for, and this kind of analytical thinking will follow your reading of literature throughout the entirety of your academic life. You should be aware of: structure, tone, form, rhetorical devices, and meaning when writing an essay that is based on close language analysis. Once you have annotated your passages, you should identify what is sometimes known as a 'leading thread'. Every essay must have a clear argument: what will yours be? Each of your paragraphs must hark back to this overarching point, and identifying your 'leading thread' in the planning stages will greatly assist your essay structure. After this comes the most important step in writing an essay: planning! Going through all these previous steps will make it much easier for you to identify three or four subpoints that illustrate your leading thread. These will make up the body paragraphs of your essay.