You could really approach this topic from more than one angle; however, there is a fairly standard way to organize a biography, since a biography is a written document of a person's life.
The best method to organize a biography is chronologically. Since a biography is a non-fictional account of a person's life, starting at the beginning of the life would probably provide details for the rest of the story. While there are other ways to organize a biography, you should stick with this method if you are trying biography writing for the first time.
Details about the location where someone was raised and what time period that person was raised in are necessary. Providing that information will give your readers a historical context. For example, if you are writing about a black person living in the south during the Civil War or a Jewish individual in Germany during the Holocaust, your reader needs to know that! Immediately, you will set a tone for the type of situation that the person was in.
How long you linger on these sections really depends upon what types of experiences the subject of the biography had as a child. You want to include meaningful chapters that teach the reader about the person. Simply stating that the individual went to school somewhere is not enough. What happened at that school that shaped him or her as an individual?
The majority of your biography is going to focus on the person's adult life. Different people might define "adult" in various ways. You need to zero in on where the significant events started to occur in the subject matter's life. Perhaps it was during college, courtship to a future spouse, or the birth of a first child. In any case, you want to open your first chapter on this person's adult life with some sort of notable event.
Keep the chapters focused, but do not make them incredibly predictable. For example, chapters entitled "College," "Marriage," and "First Child" are not incredibly original, and are probably not going to get you published, if that if your goal. Focus on the experiences that happened during those different eras. Maybe your chapters would look something like this: "How Ray Survived Modern Feminism 101," "From Courtship to Conception: A Journey Of Two Soulmates," and "Diaper Duty at 4AM." Titles like that give your readers a bit more of a conceptual approach, as opposed to a cut-and-dry method.
If the subject of your story is deceased, you should probably mention that somewhere in the biography. There are a few ways to go about approaching this delicate matter:
If the person was of a particular religious background, you could incorporate those elements as well.
Other ways to consider writing a biography, perhaps if you are more advanced in the field of biography writing, are:
The key to organizing a biography is to tell the story in a way that makes sense with the details of the person about whom the biography is written. Researching other biographies is an excellent way to get ideas of how to organize the biography that you want to write.