When writing a compare-and-contrast essay, it is important to ensure that the two things you are writing about are of the same type in some way. While it is possible to compare and contrast footballs and battleships, a paper about the similarities and differences between football and soccer seems more interesting. Also of major importance is understanding the instructions for the assignment. Oftentimes only the differences are important; other times you should discuss similarities as well.
Once you have the objects of comparison and are clear on the instructions, making lists of the attributes or qualities of the two can result in ideas to explore in the writing assignment. Noting that football and soccer both use a ball and are played on a grass field gives you some commonalities. That football players primarily use their hands to control the ball and soccer players use their feet highlights an important difference between the two.
When writing the paper, remember that the thesis statement is the most important sentence. Coming at the end of the introductory section, the thesis lets the reader know what the objects are and how your comparison of the two is different from others. For example, simply saying that two things are similar, but they have some differences may be true, but it does not engage a reader to believe that you are going to do anything more than make two lists.