Establish the most important questions you'll need to ask yourself to write this paper. Examples include, "What were this person's major accomplishments?" or "What influenced this person to become who he is?"
Find authoritative sources of information. Start at your local library. Try to find books written by authoritative and respected individuals. Then look through journals and online sources related to the subject.
Establish the basic history of the subject in the beginning of your paper. Recap the most important points concisely and establish why writing the paper is important.
Cover the most important issues. Start by establishing what those issues are in different sections. Then fill out each section with details. When you're finished, you should have a detailed compilation of your subject's background.
State your own conclusions about your subject. This can be simply a recap of your research, or it can be more opinionated, depending on the writing style required for your class.