Select a person which interests you. Biographical films require research and generally an interest in a particular person. Find out whether any films have already been made on the person you've chosen. This does not mean it can't be made again, but you should see the other versions and create something different. The Internet Movie Database generally has every movie ever made.
Find pertinent information about the subject's life. Reading a biography is generally helpful; reading two or more is even better.
Pick a story or plot line out of the biography you've read or from the research you've compiled. It's easier to write a biopic script when you center the main plot around one relationship or incident in the subject's life.
Make notes of the information you've acquired and things that stand out as essential to your plot line. Keep your research nearby for easy access during the writing.
Begin writing your script around the relationship dynamic or plotline you've chosen. Using a three-act structure as your template is helpful, even if you skew that structure later in the process.
Edit your script. After editing it, look it over again. Make sure you are satisfied. Most of the magic of film writing happens in the editing process.