Choose a subject you are passionate about. Biographical research can take years, so make sure you care about the person you want to spend time with and get to know. Ask yourself why you want to write this biography, and examine your motives. Write a proposal that will pull together your thoughts and ideas about this biography and can serve as a query letter if you plan to publish with a traditional publisher. Make a plan to complete this biography with realistic goals and time frames to guide your research.
Be scrupulous in doing your research: document where all of your information comes from, listen carefully to those who graciously share their time with you, and keep your research organized so you can find information easily According to biographer Nigel Hamilton, research is not optional as it may be for other writing genres, but rather "is the core of biography--the criterion that most distinguishes the practice of life-writing from that of fiction."
Keep an open mind. Don't dismiss things you learn that don't seem to fit your idea of this person; allow for the complexity of the human being whose life fascinates you. You may not use all the information you gather, but you do need to decide how your information reveals the person to you and what you want your readers to know. Your opinion as a biographer based on corroborated evidence is an important part of your conclusion about your subject--make it a part of the life story.
Write your draft according to the model that suits the information you researched and the focus of your biography. Examples of biography models include a partial life that emphasizes one or more parts of the life or gives a portrait of a family or relationship (see Alison Light's "Mrs. Woolf and the Servants: An Intimate History of Domestic Life in Bloomsbury"). Another example of a biography model is to present an entire life chronologically, thematically, and so on (see Hermione Lee's "Virginia Woolf" and David McCullough's "John Adams"). A mixed-genre biography is a model that could include elements of fiction and autobiography (see Hilary Masters' "Shadows on a Wall: Juan O'Gorman" and the "Mural at Pátzcuaro" as an excellent example of the mixed genre. This biography is part fiction and part autobiographical as if O'Gorman were telling the story.).
Set up a writing schedule and keep to it. Read carefully what you have written and account for any gaps in information; this may require even further research. But keep to your writing timetable.
Revise and write again. Make your work as accurate and clean as possible. Then find an editor--even if you have to pay for one--to polish your biography. Fresh eyes will save your reputation as a biographer by finding errors that will dilute your credibility. You will miss simple mistakes because of the intimacy you have with the written content.