Determine your subject. Biography essays are easiest to write when you're genuinely interested in the person you're writing about. If you can't decide, consider your interests. Remember that brilliant movie you saw last week? Maybe you want to find out more about who directed it.
Research your subject's life using reliable sources. Try to find primary sources, such as someone's autobiography, before secondary sources. Recent biographies and articles are always good, since they have the most up-to-date information. Internet sources can be useful, but only if you can attribute them to a named source.
Organize your information. You can present events chronologically from your subject's birth onward. Or, you might organize it by subject area, e.g., "Family Life," "Professional Accomplishments" and "Political Opinions."
Write your introduction in a way that grabs the reader's attention, with an interesting fact and using vivid language. "The high-flying life of Amelia Earhart, America's most famous aviatrix, is overshadowed only by the mystery of her tragic disappearance," is preferable to "Amelia Earhart was born in 1897..." This will be your main idea.
Write the body of your essay, being careful to make sure events flow naturally one after the other, and always back up your statements with facts from your research. Be careful to support the main idea from your introduction.
Write a conclusion that emphasizes the point you made in your introduction about why your subject's accomplishments are significant. Don't just restate facts. How has he or she had an impact on the world today?
Cite your sources. Consult the Modern Language Association Style Guide for help with this.