I guess you’d start by getting the consent of the person you want to write about. At first, just the verbal consent will be enough, but at some point, you probably should get some kind of legal agreement. You can’t start (or at least you can’t publish) it if the person doesn’t want you to do it, of course.
And maybe your first questions after the person consents are:
– what does that person want you to tell in the autobiography?
– what do you want to tell? Will it just be one episode after another, or will there be a unifying theme (such as how the person came to be who s/he is today because of his/her experiences or how this individual’s story was part of recent history)?
Others have already mentioned interviewing for gathering more information for the story. You’ll probably want to interview, then write a bit. This may generate some questions, which you’ll ask in subsequent interviews. Do a series of interviews to go over specific parts of the person’s life. Also, let the person talk freely – the memories may bring out others. I mean, it doesn’t all have to be Q & A. Some of it will be just listening.
You can start writing at any point, even before you get the person’s consent. Just set down the stories you already know, without trying to start at page 1 of the final book. You can sort them and fit them together once you know your outline and theme. The initial writings will be a good exercise in recounting the scenes, descriptions, dialogue, characterization, pacing, etc. You may end up rewriting everything, using these as references for yourself, or they may coalesce into a book.
When you’re ready to figure out what to do on Page 1, the outline should suggest a way. There are no rules. You can start with the person’s birth, or the person’s parent’s birth. You can start with a present-day scene, the person as s/he is now. You can start with a story that formed a turning point in the person’s life. Or perhaps start with the historical context. Find something to start with that will compel readers to want to continue reading.
Also, consider whether you want to do this as a biography, or whether you want to fictionalize it. I’m not saying you should, just throwing that out as a thought.
Post back and let us know how you progress!