Let's say you decide to write a comparison paper about New York City and Beijing, China (assuming you have familiarity with both cities). You would begin your paper with an introductory paragraph that would set up the "surprise" of your thesis: that although these two cities seem to be very different (different countries, different languages and culture), you have found that what New York and Beijing have in common is much more interesting than their differences.
If you choose to organize your paper by describing the first subject in detail and then the second subject in equal detail, you will produce two paragraphs for the body of your paper. For example, you would write a paragraph describing those aspects of New York City that would correspond closely to the situation in Beijing. (Traffic is a always a problem; many different restaurants to choose from; the presence of prestigious centers of learning; etc.) You would then follow this with a paragraph describing Beijing's characteristics that equally correspond to New York's.
Your second organizational option would be to choose several distinct characteristics and make these the topics of your body paragraphs. So for example, your second paragraph using this option would be to write something like, "The most obvious characteristic shared by both New York and Beijing is the problem of dealing with too many people and not enough public transportation," and then you would describe both cities' traffic problems specifically. Your third paragraph would discuss a second characteristic, and so on.
The first organizational option will produce a four-paragraph paper (introduction, two body paragraphs, conclusion). The second would most likely produce a five- or six-paragraph paper, depending on how many specific traits you choose to describe. (Three is usually plenty.)
In your last paragraph, you should stress again how important it is to focus on what two apparently dissimilar subjects have in common and how such an analysis can benefit us as readers (and as human beings). In what ways are Democrats like Republicans? Teenagers like senior citizens? Palestinians like Israelis? The process of exploring our similarities can be both educational and enlightening.