I'm going to take the easy way out on this one. King's next bit of advice is regarding the writer's toolbox. It should have levels, he claims, and in the top level should go your vocabulary.
Reader, and commenter, and writer, and all around awesome guy, Michael Winchell, wrote a great post over at Project Mayhem about this very topic. I'm going to point you to read that. You can find it here.
All that I'm going to add is that nothing screams newbie like reading a draft of a novel that the writer has clearly gone through with a thesaurus and upgraded the words. Sometimes it's good to hotfoot it somewhere, or to sprint, dart, hurry, or dash. But usually it's appropriate to simply run.
I greatly admire the vocabulary and general knowledge of Stephen Fry. He's intelligent, witty, and it all seems to come to him so easily. He's got so many tools in his toolbox. I have fewer tools in my toolbox. Though I love words--their origins, meanings, etc--I simply don't have the skill for retaining them that someone like Fry does. So when I sit down to write, I use what I have.
I'll admit that occasionally I go to the thesaurus on my computer. However in those circumstances it's generally because I've echoed a word three or four times on the same page, not because I'm looking to upgrade my vocabulary.
The truth is this: if I wouldn't say it in real life, I don't write it.