Research the characters thoroughly if they appear in previous works. Become familiar with their physical traits, personalities and quirks so you can remain consistent with the characters and how they communicate and interact with others throughout the book. If the characters are new, review their specifics with the person who created them and discuss how their personalities will unfold throughout the story.
Some writers find it helpful to list each person's personal characteristics and refer to them often while writing. This is especially useful if there are multiple characters.
Expand on the characters as the fictional account moves through the pages of the story. Show character growth, the generation of new ideas and challenges and more strength in reacting to adversity. Just as a small child learns and grows, so should your characters as they gain new insights and get older. The changes should not be sudden, but rather gradual shifts in each character's life.
Add other characters to the story that draw out different dimensions to the original characters. These new characters may complement or challenge the other roles in the book. Use these interactions to move your story along and make it more exciting and compelling.
You may have to adapt your story to the characters instead of the characters to the story, as is usually done. Your plot may have to be changed or adjusted and sections of the book may even have to be deleted because of the restrictions you encounter when using another person's characters in your fiction.
Keep notes on all character development for use in future works or additional volumes. They may also come in handy if a rewrite is necessary or an agent or publisher requests original notations and samples of your work-in-progress. Keep in mind that maybe someday someone will have to use your characters in her work.