Do the research. Find out what makes the subject of your biographical essay significant enough to read about. Research the person's background, school years, life-altering events, ideology and contributions to society.
Take copious notes. Include some colorful quotes and anecdotes that fairly represent the person. Note the source of each piece of information so you can make citations and write your bibliography with ease.
Plan the essay's organization. After the introduction, you can arrange the material chronologically or group it by category, giving more space and emphasis to the category that provides the primary purpose for writing the essay. For example, if the person is a pediatrician who is also a well-known poet, as William Carlos Williams was, include a paragraph or more to discuss his life as a pediatrician, but plan to devote much more space to his life as a poet.
Open with an anecdote, a quotation by or about the subject with an explanation of the quote, or with a compelling summary of the subject's significance. Throughout the essay, include in-text citations from reliable sources to establish an authority on the subject that your reader can trust.
Discuss the subject's background, then transition into the main body of the essay. The background would include year and place of birth, social status, education, ideology and life-altering events. Discussing the subject's ideology or a life-altering event may serve as a good transition into the main emphasis of the biographical essay -- the part of the person's life that is most important to readers.
Develop the main body of the essay. Include much more detail than in the earlier sections. The detail should include an examination of the subject's main contributions, including examples and quotes about your subject person and his work, as well as quotes from the subject, if they are available.
Conclude with another brief discussion of the subject's significance. You may include remarks concerning a certain event or ideology that set the subject on a course that caused him to make a difference in the world. If you do this, clearly tie in the life-event or ideology as you write the main body of the essay.