First choose whether you want to compare seemingly disparate subjects, contrast seemingly similar subjects, or compare and contrast subjects. Once you have decided on a topic, introduce it with an engaging opening paragraph. Your thesis should come at the end of the introduction, and it should establish the subjects you will compare, contrast, or both as well as state what can be learned from doing so.
The body of the essay can be organized in one of two ways: by subject or by individual points. The organizing strategy that you choose will depend on, as always, your audience and your purpose. You may also consider your particular approach to the subjects as well as the nature of the subjects themselves; some subjects might better lend themselves to one structure or the other. Make sure to use comparison and contrast phrases to cue the reader to the ways in which you are analyzing the relationship between the subjects.
After you finish analyzing the subjects, write a conclusion that summarizes the main points of the essay and reinforces your thesis.