Identify two items that you want to compare and contrast with one another. For the purpose of this article, the premise you are interested in advancing is that the character of Luke Skywalker from "Star Wars" is the male counterpart of Dorothy from "The Wizard of Oz." This premise will comprise your thesis statement, which appears at the beginning of your essay and is followed by a brief explanation of how you plan to conduct your study. In this case, your study of Luke and Dorothy would stem from watching both films and taking notes throughout.
Start with a written list of all the ways in which you believe both objects are similar to each other. Using the example of Luke and Dorothy, both of them have lost their parents, both of them live with their aunts and uncles in a dry and desolate place, and both of them believe that there has to be something much more exciting beyond the stars. Add to this list the fact that they are both being pursued by evil characters who wear black, that the power to effect change is something that already (secretly) resides within them, and that their respective traveling companions have a lot in common.
Create a separate list in which you identify all the ways in which your objects of study are different from each other. Your obvious first choice might be to say that Luke's adventures take place in a futuristic environment, while the bulk of Dorothy's adventures transpire in a magical realm that isn't defined by time or space. Accordingly, this might not be a sufficient difference to make the list. Another difference you might note is that Dorothy's companions each felt that they were missing something vital in their lives that only Dorothy could help them acquire. Luke's companions, in contrast, were satisfied with who they were and could drop out of Luke's adventure at any time if they wanted to.
Determine how you want to organize and present the contents of your two lists. One method is to establish subheadings such as "Personal traits," "Home life," "Goals and objectives" and "Friendships," then compare and contrast Luke and Dorothy within the context of each of those categories. This can either be structured so as to give each character a separate paragraph of individual analysis or to combine the comparisons within the same paragraph. Another method is to create a matrix so that a reader can see from a glance how many areas of commonality and difference exist. This would then be followed by a narrative summation of the results shown on the matrix. A third method is to create subheadings for "Similarities" and "Differences" and provide detailed examples of the characters' backgrounds, problem-solving abilities, strengths and weaknesses.
Provide a conclusion based on what you learned from comparing and contrasting your objects of study. Discuss whether the facts you obtained from your study were consistent with your original premise or whether you were surprised to discover that you were completely wrong. Where practical, explain how you plan to apply what you have learned to future experiences in critical thinking and decision making.