While Gaiman is specifically talking about how he approaches writing, all of these observations are applicable to any writer, regardless of their medium.
Here are some of his major points:
1) "Your first draft doesn't count."
This is probably the most important piece of writing advice you will ever get, not only because it will free you to face the terror of a blank page, but because it is the truth.
Aside from you, nobody will ever see your first draft, because you will never show it to anybody.
In the euphoria of having finished your novel, or short story, you may be tempted to submit it to publishers, agents, friends - DON'T DO IT! Instead, let it pumpkinate. Put it away, and come back to it after you are well into another project. Otherwise, you will never see the mistakes you have made - but everyone else will.
2) "Write even when you are not inspired."
Gaiman says to "just put one word after the other" as if you were building a rock wall. If you wait until you are inspired you will not finish your project. I agree with Gaiman completely on this piece of advice. Paradoxically, even if the muse has deserted you, once you start writing she will return. The trick is to write something - every day - in order to get the juices flowing. (It's called discipline.) Successful writers approach their work as if it were a job.
3) "Read outside your comfort zone."
Ray Bradbury also offered the same advice, and for a good reason. If you only read in your genre, you won't be exposed to different styles, different points of view, and different solutions to age-old problems. (Problem-solving is at the heart of every great novel.) So, read nonfiction, read poetry (especially poetry), read Shakespeare, read essays, read anything that isn't what you are writing. It will stretch your mind.
4) "In the beginning you will imitate other writers, but only you can tell your story."
The process of imitation is important. Those writers are your models, so choose them well. But, as you get your writing legs, you will naturally develop your own style, If you have a story to tell, your voice will shine through.
"If you don't know what's impossible, it's easier to do it ..." ~ Neil Gaiman
Ray Bradbury's Words of Wisdom - Write Like Hell!
Writing Advice from Frank Herbert: Concentrate on story