You might begin your paper by pointing out the similarities between Socrates and Euthyphro. Both men are on the verge of attending trials and have acted in ways that are strikingly unusual for society in their period. Both men also feel justified in part by their intense, personal intuitive connection with the divine. In a sense, Plato's central task in the dialogue is to try to show us that Socrates, despite apparent similarities, differs in some way from Euthyphro.
In the first main section of your paper, you should analyze Euthyphro's claims to expertise and exact knowledge and the way Socrates refutes them. It would also be worth pointing out that this is how Plato most strongly attempts to distinguish Socrates not only from Euthyphro but from his accusers, in having Socrates claim ignorance rather than knowledge.
The second section of your paper will need to look at a series of different claims made by Euthyphro. Although Euthyphro says he has exact knowledge of what is pious and impious, he does not really discuss the grounds for his knowledge beyond citing a parallel in the poets of his own actions. When Socrates presses Euthyphro to define the essence ("ousia") of piety, Euthyphro first offers an example and then the possibility that what is good is beloved by all the gods, an answer that proves unsatisfactory in light of the ways the gods disagree.
The third section of your essay should discuss the danger of not having general criteria for goodness before making judgments about whether specific cases are or are not good. Without such general principles, no one opinion is any better than any other.