I find most times my characters pick me... not the other way around. But, like a parent, I mold them into the people they grow up to be. And, sometimes, I don't succeed in making them believable on the first try. The harshest criticism I ever received was that my heroine (I forget the story, but it was a contest, I believe, posted online) was TSTL. First of all, I had to google "TSTL" and when I realized it meant "too stupid to live", I was heart broken. Did that mean I, too, was TSTL? Well, at least, I had succeeded in one respect - invoking a response from a reader - just not exactly the one I'd been hoping for...
I didn't receive that comment yesterday, but it has stuck with me. Pushed me to (hopefully) create more believable characters. The trouble is in finding the perfect balance... telling the reader what they need to know about the character, demonstrating their behaviour consistently, and, at the same time, not overdoing it. There's such a thing as too much information. The reader needs to understand what you know - on a need to know basis - without long, heavy, unnecessary verbage. Easy? Not a chance.
I base my characters' appearance loosely on real people (famous and otherwise), but I let their personalities evolve a little on their own. But now, when the story is finished, I ask that all important question - are they believable characters? And, sometimes, counter with - are they supposed to be? :) There are, after all, many "real" people who are completely unbelievable!
Happy writing/reading! And happy Friday!