An inner life. Flaws, weaknesses, endearing characteristics, a voice, opinions, a visual, three dimensional sense of the character. I create mine by mapping a life for him/her before starting my story. What's in his pocket/fridge/wardrobe, his pets, his home, his idiosyncrasies, ex-girlfriends, memories, embarrassing family members etc...
I write non-fiction. So, obviously my characters are taken from real life.
For a character to be believable they have to be real, say real things, do real things, make mistakes, and say the wrong thing sometimes. Even in fictional story the character needs to be real. Now the character could have three eyes, five legs and eight arms but still be real, the realism comes from the heart of a character.
All my characters are based on real people, some of the people I know really well, some I could just see in a supermarket and follow them around for a bit taking notes, either way they are still real people.
Dialogue that fits the character. Consistent behavior. Supporting 'actors' that through dialouge or acton attest affirmatively to the character's traits. Setting and circumstances that uphold the actions of the character.
I started of with something so simple and then I gave her abilities and then I filled in a few blanks, but all up the character must reach out to people from the very beginning.
At the moment I'm telling first hand personal stories.
I've done very little fiction, but in my reading I find that being fallible adds the most credibility to a character. Also, I think any character needs to fall somewhere on a spectrum of good and evil and never at the farthest point of either side.
To be honest, I don't know. I just do it. But I do try to become my chracter-- of course, this doesn't mean that I do things for my character, rather, my character does them, and I follow.
I have a whole system of five dimensions of character development which I won't get into in depth here, but as far as making the character believable, you want to ask two questions: What does your character want? and What is your character afraid of? There can be multiple answers for either of these. This is what is going to drive your character into action. He or she is either going to be moving toward or away from something. Also, a character needs both history and growth. He can't have been born explicitly for the story itself. There should be aspects of the character that even we as readers might not see.
My characters usually come from personality quirks of people I already know. I develop them with extensive note-taking (of course). Oftentimes, I'll have my characters fill out one of those internet surveys or make a pretend facebook profile, because then you not only get information about the character, but information in the character's own voice, which will more often than not leave certain things out.
I think characters evolve much as people do in real life: as we read on, we discover more. A believable character is multi-faceted and therefore can't be seen as a hero, except partially, if then. For me a character is revealed through dialog set against his/her actions, which are often at odds with one another. As a reader reads, he/she is always asking (I believe) "What would I do?". Great charcter development can open someone's eyes and unlock nailed-shut doors.
For a character to be believable, they have to be human. By this I mean possess both strengths and weaknesses. To me, a character is believable if I can relate to them. Everyone has to have their faults.
To create my characters, I observe the people around me, and pull aspects from them.
I usually create characters based on someone I've met or how I was in the past. I like to try to make the characters as realistic as possible. Try to make them easy to relate to or at least be able to describe to the reader why the character does what they do. Have the reader be able to get inside the mind of these characters so they can understand them inside and out. Then they have to be believable.
They need to have a flaw. I create them with much development. At first it was because I got a critic that they seems to be unreal. Then I've tried another way, is to involve myself into the character (which I think I'm not supposed to do as real writer). Sometimes it gets too deep and I didn't want to throw my characters away.
The characters names are the hardest to come up with. They are a very important to the book, common names like Mike, John or Bill just don't work for me. I came up with a key character named "Cody" which fit perfect as a killer and people like this character very much.
I think for that character to exhibit thoughts and behaviors that any reader can recognize as being quintessentially human, and even more importantly -- contemporaneous, or modern. Men and women of their times, however famous or in-famous having their mettle tested in some worldly arena. Ordinary people in extraordinary situations. Honesty, above all. Saying what must be said.
I fashion mine probably like any other author -- as reflections of myself or people I've known (or known of).