Book's background, according to the comic The Shepherd's Tale is thus (don't read if you plan on reading the comic)- his real name is Henry Evans and was born into an abusive family. He ran away and turned to petty crime before being recruited by the Independents and volunteers to be a mole for the 'Browncoats'. Evans gets a video transmitter implanted into one of his eyes to record what he sees before killing a man called Derrial Book to steal his identity. He then joins a law enforcement agency before being recruited by the Alliance becoming a high-ranking officer over time. 'Book' intentionally jeopardises a mission, causing the death of thousands of Alliance soldiers and is discharged and dumped on a nearby planet in disgrace. A few years later, he is beaten to near death by Alliance soldiers for his part in the disaster and wakes up in a homeless shelter. It is here where Evans 'finds God' and joins a church becoming a Shepherd. After ten years, he becomes a missionary and joins the crew of the Serenity.

Had to take some of that from online but I knew most of it as I read the comic a couple of years ago.This is exactly what Whedon had planned for Book in the show over time.  The comic is told in flashbacks as Book remembers them when he is dying before Mal turns up in the Serenity movie. If I recall correctly, it is told out of order so you don't really find out about him killing a dude and taking his identity until towards the end of the book......