Everyone dies. It's a simple fact of life. And when they do, many times an obituary is needed, which is just another word for biography. If you are writing one for a local newspaper or something that requires brevity, use three paragraphs. For anything else, like a eulogy or even a school paper on a dead relative, you can make it as long as you like. Just remember you are writing about someone's life and give your biography the respect that this person deserves.
Begin with the background. Described who the person was as evidenced by whom he left behind, including spouses and children. You can also include details like where he worked and what he did. Include that he was a wonderful teacher or everyone loved his Santa at Christmas; it doesn't have to be a full life story, just some interesting titbits and highlights. It doesn't have to be the Nobel Prize to be included, unless he did win the Nobel Prize.
Include personality traits and unusual or funny characteristics. If he was extremely philanthropic or donated to one cause, mention that. Give a sense of the man here -- a sense of his personality, what he found funny or cared deeply about and why people liked him.
End with the idea that his passing was sad but so many rich things came from his life. You can then end with some accomplishments of the deceased's family. Remember that research is important here. Make some phone calls to his family and friends and interview them. Just a few comments from relatives can really add to the biography.
Fact check your article thoroughly as you don't want to get any facts wrong including dates of birth and death, a list of survivors and funeral dates and times. If you are including sensitive information such as cause of death, check with the family first before publishing.