If you are a student, often the two topics used for your analogy paper are chosen for you. If this happens to be the case for you -- then you are well on your way. However, if you are not a student or if your two subjects are not chosen for you, then you must brainstorm what your explained and explainer will be.
Once your topics are selected, research them well. Some writers use a Venn diagram -- two circles which overlap -- while other writers prefer to use a simple sheet of paper with a line drawn down the middle. Either way, list qualities of each of your two subjects. Find all the facts you can, or if it is not a factual subject, think of all the ways that your topics are alike.
Once you have all the facts written down, skim over them. Then list all the ways that they are different. Typically, an analogy essay does not discuss how your subjects are different; however, this exercise will most likely help you think of more ways that the topics are alike. This will also bring out the most obvious likenesses.
Start your paper by introducing your subjects. Here you may point out how your two topics are different and how at first glance they do not seem alike in any way. The body of your work can then be approached in a couple of different ways. You may either pick three or more similarities -- write a paragraph or two about each common trait. Or you may take a more narrative slant. In any case, after writing the body, draw your conclusion, summing up the main focus of your analogy.