There is no one true approach, each working better for different people.
That being said, I thought it might be nice to present my own preferred method for constructing a character's flluff. I like to call this method the "Four Questions". This little questionnaire helps me develop a handful of basic pillars I can use as a foundation for the character, allowing me to build upon it while playing said character. The Four Questions are:
"WHO IS THIS CHARACTER?"Before delving into the more specific aspects of a character, you should figure out her most basic concept. Think of this as the elevator pitch for this imaginary person, capturing her most important elements in a simple sentence or two. It should be clear and precise, getting your point across in as few words as possible.
"WHERE IS THIS CHARACTER FROM?"Your character didn't spring forth from thin air, fully formed and ready to explore ancient tombs in search of priceless treasure. They had to originate from somewhere in the campaign's setting, a location with a interesting atmosphere and culture that more than likely left a last mark upon the character.
"WHAT IS THIS CHARACTER'S ULTIMATE GOAL?"Every character should have something important they are working towards, explaining why they've decided to become an adventurer in the first place. You have the classics, such as avenging the lost of a loved one or restoring the prestige of her long-tainted family's name. This goal can be literally anything, but should be something that will take many adventures to obtain and should be driving force for the character.
"WHAT PREVENTS THIS CHARACTER FROM ACHIEVING THIS GOAL?"There has to be a reason why the character hasn't obtained their goal yet. Maybe she doesn't know the identity of the assassin who killed her loved one, just that he had an extra finger upon his right hand, or possibly the only way for her restore said prestige is to hunt down and kill the dragon her ancestor failed to slay many years ago. This is where you give the GM a very blatant hook to use within the campaign, something to draw them into the story the group is attempting to weave together, making the challenges just a little bit more personal.