This, to me, is mainly about what they call "frame". During preparation, you get to know your characters, and during writing, you totally take on their "frame", which is the context they put the world into. How they feel and what they see through their own eyes.
It's not easy to decribe what I'm trying to describe here ("frame"), but as one writes more and more, he/she gets into the habit of taking on different frames easier. I also think that the problem for many people is a lack of preparation - they just don't know their own characters well enough by the time they start writing.
Additionally, it helps to talk to a lot of different people with a lot of different personalities - and by that I don't mean you should only talk to schizos!
When you are at the dinner party, talk to that self-absorbed business man who can only talk about his business, try to soak up his personality, the way he perceives himself, the way he perceives the world, the way he judges, the way he takes decisions! Then next time, talk more to your brother-in-law, who is a day-dreaming artist-type and painter.
You have a lot of opportunities in life to do this, for everybody's favorite topic is themselves! People love to talk about themselves, and you just sit in and listen. That job is similiar job to a bird watcher's...
Hope that helps.