This moment comes, when you open a new game, with new characters and all, and you all sit across the round table and wait for the ordinary world to disappear and for the imaginary world to fill the space. You, like every person wants to get into the mind of your character, you want to be him/her and not yourself anymore, at least for a few hours.
The GM starts to speak. She describes the setting, going over all the details of the bar that you're within, of the tired barkeeper and of the stinking man with the purple roses who's supposed to be some kind of a magician. Then he asks you: "What are you playing?"
And in a moment, everything that she built is lost. In a moment, you're not Beatrix anymore but only play her. The shift is too quick, too strange, too out of its place. You look at your wonderful GM with your eyes and she suddenly understands what mistake she made. She quickly corrects herself: "Can you please describe yourself?" And the change is far too great. Suddenly, you're not Eleanor anymore, but Beatrix.
She then continues to one of her old tricks, and she asks you (just like she asks everyone else) a question about Beatrix. Not a familiar question, but a strange one. "What does Beatrix do every Sunday morning?" Last story opener she asked you about Lisa's marriage life, and she asked Bob's character about what he liked best in his wife. She didn't ask Bob, as she didn't ask you, she asked the characters. Suddenly, you were in the characters' minds, thinking like them. The shift was well familiar, and it felt great.
Today, it's the time to start a new session, and you begin in the same way your old GM opened the game. The players respond well, and you can see that they begin to be their characters, to come into their skin, to sit into their brains, just like the way it happened to you.
I don't know if I succeeded with what I tried to pass here. I hope I did. It's not magic, and Eleanor didn't lose touch with reality (although she wasn't real in the first place...). It just helped this Eleanor to be her character for a few hours, and to leave the troubles behind when she met her friends...
How about you? How do you help the players to be their characters?