What do philosophy essay topics look like? There are, very roughly, two basic kinds of philosophy essay topics: "text-focused" topics and "problem-focused" topics. Text-focused topics ask you to consider some particular philosopher's writing on some issue. (eg "Discuss critically David Hume's account of causation in Part III of Book I of his A Treatise of Human Nature" or "Was Wittgenstein right to say that 'the meaning of a word is its use in the language', in his Philosophical Investigations, Sec. 43?"). Problem-focused topics are more directly about a particular philosophical problem or issue, without reference to any particular philosopher's text. (eg "Is voluntary euthanasia morally permissible?" or "What is scientific method?")
There is another sort of topic, one which presents a statement and asks you to discuss it, where that statement is a "made up" or, at least, unattributed quote. (eg. "'Without belief in God, people cannot be moral'. Discuss.") I shall regard these as variations of the problem-focused type of topic. Where you are asked to discuss some such statement "with reference to" some specified text or philosopher, then that topic becomes more text-focused. (eg "'Without belief in God, people cannot be moral'. Discuss with reference to J.L. Mackie's Ethics: Inventing Right and Wrong.") Occasionally, a topic presents an unattributed statement, but the statement is, in fact, a quote from a particular philosopher you've been studying, or, at least, a good paraphrase of their thinking. (An example of the latter: "'All the ideas in our minds originate from either sense perception or our reflection upon sensory information.' Discuss.", in a course devoted to John Locke, whose views are summed up in the quoted statement, though those words are not actually his.) Should you take such topics as problem- or text-focused? Rather unhelpfully, I'll say only that it depends on the case. You might ask your lecturer or tutor about it. Whichever way you do take it, be clear in your essay which way you are taking it.
The difference between text-focused and problem-focused essay topics is, however, not very radical. This is because, on the one hand, any particular philosopher's text is about some philosophical problem or question, while, on the other hand, most philosophical problems (certainly virtually all those you will be given as essay topics at university) will have been written about by previous philosophers.
The basic way to approach text-focused topics, then, is to treat the nominated text as an attempt by one philosopher to deal with a particular philosophical problem or issue. The essay topic will, generally speaking, be inviting you to do philosophy with that philosopher, to engage with them in thinking about the issue, whether that engagement proves to be as an ally or an adversary. The chosen text will usually be one which has been (or deserves to be) influential or significant in the history of philosophy, but the task is not to pay homage to past masters. But, even if homage is your thing, the best way to do that here is to engage with the master philosophically.
With regard to problem-focused topics, you will often find your exploration of the problem aided by taking some text or texts which have dealt with it as reference points or prompts. This is not always strictly necessary, but many of you starting out in philosophy will find it helpful to do so - it can help you give focus to your response to the question. (Thus, you might, in an essay on the topic "Is voluntary euthanasia morally permissible?" take it upon yourself to use, for example, Ronald Dworkin's Life's Dominion and Peter Singer's Practical Ethics as reference points. Or, in an essay on the topic "What is scientific method?", you might set up your answer via a comparison of the two different accounts in Karl Popper's The Logic of Scientific Discovery and Paul Feyerabend's Against Method.*) How will you know which texts to adopt as reference points or prompts, if none is mentioned in the essay topic itself? One way is to consider what texts have already been mentioned with regard to the topic in your course reading guide and in lectures and tutorials. Another way is to do some of your own research. On this see Section 4 below.
* In this guide, in giving examples of how to go about answering an essay question, I am not necessarily giving any concrete or reliable advice for any particular topic. The examples are primarily to do with the form or style or strategy you might find helpful.