I got an email this morning from a woman wanting to know how to get started writing personal memoirs. She had met some people over her life who had had a big influence on her and she wanted to write their stories.
First, there are two possibilities here. One is writing the personal story of another. A recent editing client, Bill Bacon, sent me a wonderful manuscript about the amazing story of how his parents met and fell in love. He had filled the short volume with wonderful photos and was going to publish it himself. While he is a bit player in the story (he mentions how his mother told him some of the details), this is not Bill's memoir.
There are several things to do as you prepare to write a personal story. One is to interview any persons involved in the story, especially those with major roles to play or those who knew the person who is the subject of the story. Then you gather any written documents (letters, diaries, emails, publications if they created any) and you read those and take notes of pertinent information. You also gather photos if that is helpful to you or part of the finished work.
When you write a memoir, you tell your own story and include as characters those you have met or have influenced your life. The research can be similar to personal story research except that most of the written documentation is your own: your correspondence, your journals, your photos--anything that will help you remember.
It is always extremely helpful before you begin writing to immerse yourself in the genre by reading a variety of kinds of personal stories or memoirs. Both are very elastic forms of literature and you'll get good ideas by seeing what others have done. It's also helpful to be well-grounded in story-telling by reading lots of short stories and fiction so that you can handle dialog, description, and narration.
Like most non-fiction, memoirs and personal stories can be organized by chronology or theme, but in neither case, do you need to start at the beginning. I began my memoir, Sober Truths: The Making of an Honest Woman, by writing stories about significant events in my life in a rather random order and after I'd written about 60 of those, I began to piece them together with themes and chronology.
All that said, if your goal is much simpler, to write a story about a friend so you don't forget, then just go for it! Your friend will treasure whatever you have to say.