Start with the facts, the simple facts.
Then research more generally the period, the places, clothing, society of the time, seeking to put the person in context.
Then look for what contemporary people wrote about the person and check the press.
Now look back to the chronology of events and look for patterns in the subject's development: why did they become the person they were? what inner struggles did they experience? what epiphanies did they reach? how did they conquer the obstacles in their path? how did they suffer?
Try and get 'under the skin' of the subject and understand her/his life from the inside out.
Now brainstorm and draw up a 'mind map' of all your ideas.
Now pick out the most interesting lines and patterns and threads and begin to weave them together as a narrative.
Consider your style and make it appropraite to your subject and your intended readership.
Write your first draft.
Get it critiqued.