Read the question you have been given. Is it both compare and contrast? If it is only compare, then you do not need to contrast. Many students misread the title, and therefore do not fulfill the title of the essay. Make sure that you are doing exactly what the questions tells you.
Read the two works and highlight key words or phrases. Take notes on the subject, the context and the content. After doing this, some areas of similarity and difference will appear. Find four major areas of similarity or difference. They can be the themes of the work, or the types of language used or an argument advanced.
Write the four areas you will be focusing on, and find quotations to support your assignment. Use the areas you highlighted before as a guide. Read books about the original works and see if they contain information on your particular theme. For example, if one of your themes is comparing the role of women in "Macbeth" and "Hamlet," a book on feminism in Shakespearean tragedies would be a good place to start.
Write the introduction to your essay, giving a brief synopsis of your thesis, including what you will use to advance your argument. Follow these with your four paragraphs and then make a conclusion, such as whether the works are more similar than they are different, or whether they are different owing to a particular reason. For example, when comparing "Hamlet" and "Macbeth," you may conclude that their differences stem from the fact that Hamlet attempts to gain a crown which has been usurped, whereas Macbeth is himself the usurper.