Previously established creatures
Question: I want to write a book and use a previously established creature and universe. What kind of permissions do I need?
UPDATED: Generally, if your source material was the creation of an author who has been dead for 70 years or more, you may not need permission to borrow from it. However, you need to check this out first, because in some cases copyright can last for 95 years after an author's death. Also, copyrights can be owned by corporations for longer terms.
Anyone can write a story about mythological creatures and characters (e.g. vampires, werewolves, Zeus, Paul Bunyan, etc.), historical characters who have been long dead (e.g. Julius Caesar, Socrates), or fictional places in very old stories (e.g. Atlantis, Lilliput).
However, if you want to set a story in a universe created by an author who is still alive or only recently deceased, the short answer is... DON'T. At least, don't do it and then try to sell copies to other people or submit it to a publisher. To do so without written permission may be an infringement of copyright and you could get yourself into trouble.
The exception is that most authors will allow fan fiction, provided that you distribute it free of charge and make no profit. Authors have a right to stop fan fiction as well, but they usually don't because it promotes their original works and because fan fiction usually doesn't cut into an author's revenue for the original work.
Another issue is trademark. Some characters (for example, comic book superheroes) are trademarked by the publisher. So even if the copyright on the original stories has lapsed, only the publisher that owns the trademark on a particular character can publish stories about him/her.
If in doubt, it's best to create your own universe and characters, even if they bear some superficial resemblance to others. You cannot go wrong by being original.