Decide how to write the author biography. There is more than one school of thought on this issue: the lineal, and more conventional biography which begins with the author's parents, his birth and childhood. Or, you could progress in a more unconventional, and perhaps unpredictable fashion, beginning with a penultimate event in the author's life and working in either direction from that point on, or in any direction you choose. A fine example of the more conventional and lineal biography is David McCullough's biography of John Adams; whereas an example of a more unconventional biography, where the author "purposefully blurs the boundaries of past and present", is John Bayley's biography of his wife, Iris Murdoch.
Read the works of the author in a chronological fashion. This task can be difficult for some writer's works. For example, the order in which the works of Jane Austen were published were not necessarily the order in which her works were written. By reading the author's works chronologically, you are able to see how the author's mind and style develop, which is useful and interesting information to have when you write an author's biography.
Explore the lives of the author's parents. How the author was brought up can affect the manner in which the author lived his life and the choices he made. It is up to you how deeply you wish to pursue this information, but it cannot be discounted or ignored when you write an author's biography. If the author is contemporary, then you can interview people who were in the circle of the author's parents. If not, then you must rely on private letters, correspondence, as well as articles published about the author's parents. You may have to ask permission to have access to private papers.
Research the childhood of the author. If the author is contemporary, this task is made easier in that you will probably be able to find people to interview. Talk with anyone you can think of: friends, fellows, countrymen, teachers and the like. If the author is historical, look for private papers, journals and letters. Some of these items may be public domain, but more than likely you will need to gain permission to have access to them.
Learn about the author as an adult. You can rely on the sources listed in steps two and three, but you should also consider exploring the author's private library as well. Examining what is in the author's library is almost like having access to the author's mind, in that you will be able to see, plainly displayed, the subjects that interested the author, and which books were favorites and best-loved. All of the above will help you in creating a full and complete portrait of the author as a person.
Read biographies that have been written about the author. Other biographies may have clues about the direction for further research in your own work. You may be able to gain some useful information by looking at the bibliography of these works as well.
Compile the information you have gathered, and put it in the order you desire as you write an author's biography. If you have done your research thoroughly, you will be able to create a rich biography of an author that may be read for generations.