Sarah Stone and Ron Nyren in their book, Deepening Fiction, tell us that a character is a constellation of very particular traits and attitudes, and when these traits and attitudes coalesce into a harmonious whole we have the essence of that character.
There’s a particular way your character enters a room full of people, the strangers he makes ready eye contact with, and the strangers that he ignores. Ask yourself, how is your character with people from the opposite sex? Is she quick to take offense? How do you know when she’s annoyed? Does your character overeat when he’s stressed, or does he look for a fight? When her feelings are hurt, does she cry or swear up a storm? What would it take for your character to fall in love, get mad, give up hope? What makes your character laugh?
Now make that very, very particular. Using the example of what makes your character laugh, think of three people in your own life. What makes them laugh? Then ask yourself how each of them laughs?
If you’re starting to build a character, take one of these reactions and a write a paragraph or a short scene in which your character is embarrassed or busts out laughing. Write it in third person, so that you as the writer can see what your character looks like and sounds like. Then try to write the same scene in first person to discover what it feels like. Try to use as many particular and sensory details as possible. I find that if I sink my character deeply enough in a scene, she will reveal herself.
This same exercise works beautifully for rounding out an established character in your on-going project.