In the interests of being comprehensive, I am going to discuss comparison and contrast, since quite often students are assigned to write essays in which both must be done. I am also going to focus only upon structure, because I do not know what stories you are expected to compare.
First, what does it mean to make a comparison? It means that you are looking at two "things," in this case two stories, perhaps, and determining how they are the same. You might, for example, be able to point out that two stories had similar settings, that two stories had male villains, or that two stories used rivers to symbolize journeys. These are the kinds of elements one looks for in such an analysis.
Second, when we contrast elements, we are looking for differences. Again, in two stories, the events might take place hundreds of years apart, one may have a happy ending while the other has a tragic ending, or one may show a successful protagonist while the other shows a failure.
If you are meant to write a comparison only essay, this can be structured with an introduction that states the stories you are comparing and what elements are similar. Provide a brief description of each story in the introduction, too, for a reader who might not be familiar with them. You can then go on to develop body paragraphs about each similarity, and then finally write a concluding paragraph that reminds the reader what the similarities are. If you are meant to write a contrast essay, you would do the same, except your thesis would focus on differences.
If you are expected to write a compare and contrast essay, there are two methods of structuring this. For both methods, you must write an introduction and conclusion. It is the body paragraphs that will differ.
The first method is the point by point method. You decide what elements in the stories are similar or different, and you discuss each element in a separate paragraph. For example, you might discuss settings, symbolism, and conflict. Your first body paragraph would discuss how the stories are similar or different in their settings. You would repeat this analysis, similar or different, for each element you want to discuss.
The second method is called the block method. This means two body paragraphs, one discussing all the ways the stories are similar and another discussing all the ways the stories are the same.
So, in summary, to write a comparison essay, you will find the points in which two stories are alike, while to write a contrast essay, you will find the points in which the stories are different. But to write a compare and contrast essay, you must look at similarities and differences, using the point by point method or the block method as your structure.