When I do my outlining for a new WIP, I write up a lot of backstory. I also do character sketches, to help me have a definitive idea of each of my characters - not just hair color, eye color, and favorite movie, but what they would do on a perfect spring day, where they would go on vacation if money was no object, and - come to think of it - how they feel about money, in general. This is a fairly standard practice for character building, but I feel it only gets me so far.
That's why I've taken to writing first-person narratives - letters to me, if you will - in the voice of each character. These narratives generally address the main conflict faced by that character in the story, and how she or he feels about it. Does she believe that the problem is insurmountable? Does she still have hope? Who is she counting on most to help her? Who does she expect to cause her the most trouble?
I also write first-person narratives by all individuals involved in a romantic relationship in my story. For each one, I ask the character to tell me:
What do you love most about this other person?
What would you miss the most if he or she were taken away?
When did you first feel an attraction and what triggered it?
And, well, I'm sure you can come up with a lot more questions along this line.
When I wrote FIREFLY, I referred to these narratives constantly. They helped to maintain consistency within a character, but they also helped me see that, despite consistency, all well-rounded characters have internal conflicts they are dealing with. People are filled with contradictions. Your characters need to be, too, if they're going to leap off the page as real people with real complexity.
When you ask your character to tell you how he feels about the central conflict, chances are his answer will be complicated. It won't just be as simple as, "I hate my father and wish he were dead," because where's the true conflict in that? Nothing is ever that straightforward. If it were, in chapter one your character could pull out a shotgun and shoot his father and the story would be done. Instead, your character's answer to how he feels about the central conflict will be layered, complex, and in some ways, contradictory.
For you, as the writer, the secret to your character's arc lies hidden in these contradictions. Early in the story your character may respond most to the tug of one attitude toward the central conflict. But as the story moves along, he may feel the influence of another attitude toward that conflict, and he will begin to change. By the time he's completed his character arc, he may find himself in a place of compromise between these two contradictory attitudes.
So ask your characters questions. If they give you canned answers, or if they don't want to talk, find out why. Make them open up to you. Read your characters' diaries. (I won't tell on you!) In life, prying into a person's secret inner world might be a no-no, but in creating authentic characters, it's essential. Your readers will be thrilled that you did.