Re-read the parts of the book, or books, where any biographical information might be about your character. Usually this is in the beginning of the book or when the character interacts with either a new character or remembers a character or scene from the past. If the character is in multiple books, such as Jack Ryan in most of Tom Clancy's novels, the biographical information is spread out and revealed over time through all the books.
Write down the information you come across. For many good characters, such as Jack Ryan, you can find out everything from birthplace to their families' names and sometimes their hobbies and pet peeves. For instance, in "Hunt for Red October," Jack Ryan has a daughter who wants a baby brother, or a teddy bear, brought back while her dad is on his latest assignment with the CIA. He is an intelligence analyst who writes books. In this book, it is revealed he wrote a book on Admiral Halsey and has friends in the submarine field of the navy.
Write a biographical sketch of the character using the information you found. You can also make notations of where in the book you found it and what the situation was to make the characters more appealing to others who may not know the character.
Complete the piece by tying all of this information together using an informal tone as you would when writing about a friend. Most favorite characters are like friends to the readers who love them. You are simply introducing a friend to others so that they would want to know your friend as well.
Write about your character's lifestyle, his clothes, style, actions and reactions in certain situations. You can also include his appearance such as his build, skin color, age and other information that brings the character to life. If your favorite character has a certain saying or item they use as a trademark, include that as well. Sherlock Holmes has his pipe, and Huck Finn has his straw, while most of the characters in Alex Haley's "Roots" speak broken English and abbreviated sentences.
Make sure to write for brevity while attempting to include as much information as you can. Your favorite book character's details will take up lots of room. Consider the length of a book review, usually under 1,000 words; your character's biographical sketch should follow this length as well.