Is it possible to copyright your homebrew world that same way you would copyright a book or another piece of writing like a song or speech? Would I need to completely exclude any sort of Pathfinder and/or D&D rules from it?
Technically, any creator of anything automatically has a copyright on any non-derivative work.
The question really has to start with "What do you want to do with that copyright?"
1) IANAL (I Am Not A Lawyer).
2) You have copyright on any original, creative output, so yes.
3) You would need to exclude PF/D&D stuff that hasn't been put under a license permitting others to use it. I haven't looked into the OGL (Open Gaming License) but I think that's what that does. I believe PF is largely under the OGL, but Golarion certainly isn't---that's why d20pfsrd always changes the names of Golarion-specific material. You definitely want to read the OGL if you pursue this at all, I imagine it's somewhere on paizo.com.
4) DIMTIANAL? (Did I Mention That I Am Not A Lawyer?)
With the "I am not a lawyer" disclaimer:
1) Copyright is automatic. If you wrote a creative work then you have a copyright. Doesn't matter what it is, so long as it meets some very minimal standards. So yes, you already have a copyright.
2) Your work is derivative of the D&D/Pathfinder games on which it's based. This doesn't mean you don't have a copyright, but rather that your derivative work may infringe their copyright. An individual work can be covered by multiple copyrights. This means you'd need permission from the copyright holder to publish your work. In this case that's relatively straightforward, since the Open Gaming License serves as a standardized way by which you can use 3E D&D and Pathfinder rules without having to actually negotiate with the rightsholder. Follow the rules of OGL, and you're allowed to use the content covered by it (which isn't everything).
As the above. When you make something, it's *yours*. From what I understand, written works are even more protected than other things.
If you want a little security, mail your stuff to yourself and don't open the envelope. That way, you have officially dated proof that you are the author.
You cannot copyright ideas. You can copyright the physical expression of those ideas (music, art, books, etc).
So, if you write a description of your world, you have a copyright in those particular words in that particular order, but not on the idea of "a planet with methane ice" as your world.
Be sure your monsters and inhabitants and place names have no relationship to anyone else's names for monsters or inhabitants or place names.
For example, you can't include "hobbits" in your world, but no one can copyright the idea of small humanoids who love adventure and good food. As long as you call them something else and don't use Tolkein's description of them, you can have small humanoids.
And, don't confuse trademarks with copyright. Often you are infringing on a trademark, not on the copyright, when you try to incorporate someone else's named character in your world.