Believable characters aren't perfect. They screw up, they have quirks, heroes get the erge to do something they know they shouldn't, and sometimes will. They will alter their behaviour in different situations, based on if they're with strangers or people familiar, and even how that familiar person knows them could alter their behaviour. They have problems, some that they can't fix. Really, just think about how you behave on a daily basis, or how your friends behave depending on whether you're alone or there is family around. Think of what politicians say in public, and then what they're caught saying private.
There is no 'formula' for writing believable characters, because then they would be sterotypes. And stereotypes are hollow, off the shelf templates, therefore unbelievable. The only way to write a believable character is to make them complex, flawed, fallible beings with odd hangups and strange tastes, dislikes and grievances. I find the best way to do this, even if it is only subconcious, is to base them on real people. You can build up your catalogue of real human behaviour and characteristics by people watching - I do it all the time, whether it is people I know or strangers at a bus stop. Observe, make mental notes, file away what you find interesting or different or funny about people - but don't make it too obvious ;-) And never, EVER write a direct like for like characterisation of a real person. You will always get found out ;-)
To make a real character, you have to think of him or her as real. I see my characters as different people in my life, with a few different features of course, and of course the main characters often come from my own personality. Amongst other possibilities, I often try and put my characters in certain situations, however irrelevant from the story, and if I'm able to get into their minds, then their responses will seem completely natural, and their characteristics as normal as if they were real people. It's a bit difficult to word and understand, but it's a technique that works for me and a few other people I know.
^ I think of mine as real as well. I imagine my characters in situations from my life, and wonder how they would act in my stead. I delve into their past and see what made them the way they are today. Getting to know your characters as you would other people is invaluable.
I ditto most of what is said above, and the only thing I would like to add is that 'contrast' can be a way of bringing your char to life. By that I mean put a next-door-boy/girl type char in a superhero situation (extraordinary situation). For example, a meak and mild char is the only person who can safe the human race, or put a superhero type char in an ordinary situation, example, a handsome and ambitious man working as a clerk. Simply put, the wrong person in a wrong situation. It will give you a chance to think how will he/she react and make you understand your char more deeper (it will give you a lot of conflict as well) You can give your chars quirks and traits, but those are not the only things that make a char 'believable'. Give few quirks and traits, and develop them throughout the story, instead of tons of quirks and traits. And of course, knowing the inner most desire of your chars is a must.
I would agree with what mamma said, to a point. I don't think I would advise using characters from movies or television as a blueprint. However, one of the best tools you can use to add dimension to your characters is to watch people. Keep a journal of interesting, quirky, sweet, compassionate, deceptive, just plain not nice things people around you do. These are real-life people. This is the way real people behave. As you are writing your characters' situations think about whether he or she would do this or that and ask yourself why. And remember, being human is a disease. It is a terminal illness. Human beings are fallible. They sometimes do silly or irrational or dumb or just plain spontaneous things. They also get colds,stub their toes, suffer Freudian slips. Even the best of us can be snarky, unkind, or unintentionally rude. it is the combination of all of these things that makes your characters 3D 98.6 people. Good luck.
sorry i wasn't specific enough... obviously [i'd hoped], in re movies/tv i meant the many fine, well-drawn/written/acted ones, not the sadly many more there are of the opposite quality... if one is writing fiction, it can be extremely helpful to see fictional characters brought to life, especially when in a time and setting writers can't possibly study firsthand for themselves, such as with historical fiction, futuristic sci-fi, faraway places and societal/cultural groups they have never been to/have little/no personal knowledge of... a writer born and raised in the northeast, for instance, who's never been south of the mason-dixon line, but wants to write a historical novel about the south in the early to mid-20th century can learn a lot about how people there behaved and spoke by not only reading the works of tennessee williams, william faulkner and harper lee, but also by studying those characters in semi-real life on the screen, since most of those works were made into exceptionally fine films and realistically enacted by some of the most talented actors of our time... so, i stand by my advice to also study tv and movies, when developing fictional characters you can't observe and study in real life...
Research psychology. Even if you're not a psych major like me, you could try taking a couple psychology classes, or just reading psychology stuff on your own. In particular, researching the closest real-life analogue to your character's experiences, to see how people usually react and why. (For example, I always thought it would be very hard for a mother to love a child conceived by rape and nearly all such children would be aborted if possible, but this study suggests it's more complicated than that.)
A good writer needs to understand people. The best way to do that is start understanding yourself and being brutally honest. Once you've done that you can see how much people perceive themselves as opposed to the truth, how they deceive themselves, see how their flaws affect their behaviour etc. A good writer is a student of human behaviour.
i would have to add 'fiction' in there, before 'writer' in order to agree with those statements... there are many other kinds of writer, after all... and one doesn't necessarily need to be a student of human behavior to be a good technical or science writer, for instance...