At one time, we all wrote like we talked. Of course, we were only six or seven years old when we had this amazing talent. Years of formal schooling have chased the gift away. Still, conversational writing can be found in movie scripts.
You'll see contractions and sentence fragments when you read a movie script. Why? Because that's how we talk. So if you wanted to learn how to write in this fashion or learn more about story, you might take a class called Writing Dialogue for Emotional Impact at the Writers University taught by Karl Iglesias. And his book, Writing for Emotional Impact, is an excellent read that serves up fresh writing techniques.
For those who are interested, here's a dramatic scene I've written for a short story after taking one of Karl's lessons.