Decisions are written by one justice "for the court" or "for the majority." Other justices may write additional opinions concurring with or dissenting from the binding majority opinion. The decision in Plessy was written by Justice Brown. Since this is a class assignment, I'll stop short of saying anything about him. However, there is a biography of him in Clare Cushman's Supreme Court Justices: Illustrated Biographies, which may be in your library. As a good resource on the story of the case, you might look at Cheryl I. Harris's chapter about it in Dorf, Michael C. (2010-05-12). Dorf's Constitutional Law Stories, 2d (p. 187).

edit: It is pretty widely held that the most interesting thing about Plessy is Justice Harlan's dissenting opinion, so don't miss that.