Write your story in first-person narrative to allow your protagonist to explain her past to the reader. Example:
Who'd have thought that a small town murderess like myself would end up being courted by the most eligible and richest bachelor in Chicago? And yet here I am. No formal education, the social graces of a moose and a nasty knife wound from Husband #3. One can only hope my new amour is too besotted to notice and too gullible to question my replies.
Throughout the story, the character can interject introspective remarks that fill in more pieces of the puzzle.
Incorporate conversations between other characters that will make your reader feel as if he is eavesdropping. Example:
"Whatever you do when Henry arrives, don't get him started on why he quit a perfectly good job with the family firm and ran off to New York. He likes to tell people that it's because he fell madly in love with somebody and came crawling back when she broke his heart. The truth is that he thought he'd make it big on Broadway with his stupid little play -- the one he wrote in high school? -- and they thought it was as stupid as we did."
Throughout the story, characters can reference other things Henry has done by talking behind his back or teasing him with memories he would just as soon forget.
Insert flashbacks that are triggered by specific events in the present. Example:
"Come on, Jenny! The water's not that cold." They were all in the pool by now, daring her to dive in and join the fun. As she stood on the diving board, the unbidden visions she had tried so hard to block out for the past 15 years made their vicious return. The same sort of day. The same sort of laughter. The same swimming pool. Jenny closed her eyes, knowing that when she opened them she would look down and see once again the dead body of her little sister.
While flashbacks are effective in creating character backstory, use them sparingly so as not to put the momentum of the present action on hold for too long.
Utilize monologues in which characters confess their past deeds to others who are pressing them for the truth. Example:
"I've loved you from the first moment I saw you, Margaret, and I always will. To act upon that love and marry you, however, would condemn you to an existence beyond your darkest nightmares. My family is not of this world, my love, nor even of this century as I've had you believe. A curse that was put on us over five hundred years ago compels us to feast upon the blood of others in order to survive. I would rather walk away from you forever than to make you as feared and hunted as I am."
These "confessional" revelations can also be spread out over multiple dialogues and are an effective way to unpeel layers of suppressed secrets.