Choose an interesting person to write about. This is the most important step in the process. Ask yourself, if readers don't know this person, would they want to read the biography you write.
Interview your subject and/or complile your information. The more information you have the better.
Select a tone that matches the subject's personality. For example, is it a sad, inspirational, dark or gritty story? Use this to guide what events/information you will write into the biography.
Outline chronologically from birth to death or current day.
Break your subject's life into three or more arbitrary pieces/periods. Search for plots and subplots within these parts.
Choose a starting and ending point that provides the most resolution and the best plot arc. For some this is from birth to death or current day, but many times your book is more interesting if you focus on a specific time in the subject's life. For example a professional athlete's biography may only focus on the subject's time as an athlete.
Write. Shoot for 40,000-100,000 words on the pages.
Join an online or local writing group. Share your work. Their editing, critiques and feedback are a way to make your biography great. No one writes a masterpiece alone.