How much of your character's back story do you know before the story begins?
Do you know everything or just the basics? -- Bobby Nash
There are two opposing ways of thinking about this, as opposite as democrats and republicans are politically -- at least in my experience of meeting and talking with writers. The members of one group tend to make it all up they they go along, reinventing their characters almost willy-nilly with every twist and turn or plot and nuance of story. On the other hand, the members of the other group keep their folders of notes and printouts and family tree diagrams handy near their computer desk or (for the tech-obsessed authors) in a spreadsheet on the cloud so they can't lose the information at home and can have it readily available even when they're not at home.
Many, however -- and I'm certainly one of them -- fall somewhere in the middle. I like to know the basic personality and major life experiences for my core characters, but I tend to fill in the details for other things (like what college he attended, who was her first boyfriend, is he allergic to gluten, where did her tattoo come from, for example) as I'm writing and as the story dictates. It's funny though how often some of those minutia of details can become key plot points in a story or triggers for a new story for a future volume featuring the character in some cases.
A real-life example: When I came up with the Victorian detective for my story "Death with a Glint of Bronze" in Dreams of Steam II: Brass and Bolts (Amazon, B&N). I knew that within the scope of my 20 or so pages, I wouldn't need to dig so far into McKendrick's past to know about the facts and dates of his previous marriage or how long his time as a soldier in India was exactly. But I did need to know all the details of the accident that took one hand, and the childhood malady that left his other hand palsied. Those were the important back story details. Those were the ones on which the story hinged and swung.
I used to do questionnaires about my characters, and I think those kind of details are good to know, and I still recommend them as character exercises for beginning writers. (I have an online tutorial about character development at http://taylorverse.com/tutorial6.html that goes into detail on those kind of exercises.) However, after writing for a nearly 20 years now, the questions that lead to those kind of details have become internalized, and I no longer have to make a conscious effort to fill out questionnaires or apply for jobs as my character. As the characters become real in my head, those specifics become automatic, and sometimes even just held in my subconscious until such a time as they are needed for the story.
A caveat -- the longer the work, the more information I've learned that I need to know upfront about the back story. Why? Because I've found that those are the kind of details that help carry a story beyond the simple plot point A leads to plot point B leads to plot point C, etc. kind of story. Those are the things that take a story (at least for me, you're mileage may vary) from a mere skeleton to a flesh and blood living being.