A compare and contrast essay is used to show how two or more subjects are similar and how they are different. When you compare, you are highlighting similarities; to contrast means to explain the differences.
To organize a compare and contrast essay, you need to decide your approach. You could decide to explain all the similarities first, then review all the differences between your subject items. For example, if you were writing about cats and dogs, similarities would include both being mammals, having four legs, and being popular domestic pets. Differences could be that dogs are generally larger, that cats have better night vision, and that dogs are more easily trained to do tricks than are cats.
Another approach would be to take one idea and show how your subjects are the same or different regarding this one aspect, then move on to another aspect and explain the similarity or difference for that part of your subjects. For example, you could start by explaining that both cats and dogs were mammals; next you could state that both are popular pets; then you could write about the breeds of omesticated dogs that are much larger than pet cats; followed by the better night vision possessed by cats as opposed to the superior sense of smell possessed by dogs.