Research the subject of the biography. If the subject is still living, you should try to interview her directly, as well as close associates, recording all conversations. If not, interview as many direct relatives and friends as you can. Also scour archival resources, such as personal documents, photographs, recordings and newspaper articles.
Compile an outline for the biography. Focus on the issues, questions and topics in the subject's life that interest you. Most biographies are linear, but a major exception is Hermione Lee's "Virginia Woolf," which is divided into chapters on major topics in Woolf's life.
Write the biography. With an outline in hand, you can work on different sections of the biography at the same time and also keep the larger picture and scope of the work in your mind. Keep your audience--whether popular, niche or scholarly--in mind.
Source all information scrupulously. Footnoting your information correctly is one way you can maintain your credibility. All quotes and psychological claims should be footnoted.
Put together a list of agents and publishers that represent biographers. Start with companies that publish a large number of biographies, reaching a wide, international audience.
Send query letters to agents and publishers regarding the biography. The query letter should outline your qualifications, the importance of the book, and your contact information. Start the letter with a hook that enthralls the audience.
Negotiate a contract with an agent or publisher that becomes interested in the biography. Work through revisions and address any concerns. Once completed, you should have a publication date set.