When you first start writing this seems like a non-issue, but the more you write, the bigger an issue it becomes, especially when you write longer works like novels or novellas. I personally prefer to write book-length fiction, and while I have at times written short stories, I make it my policy to always have about four books in various stages of completion (some never do make it to total completion!) So how does one keep all that organized?
It all depends on what works best for you, of course, but my system involves at least three three-ring binders. I always do my first drafts longhand. I don't know why, but something about putting pen to paper (as opposed to fingers to keyboard) is psychologically comforting, and seeing the pages fill up gives me a sense of accomplishment that watching a Word document grow does not. So the first binder contains my handwritten manuscript.
That said, of course the longhand manuscript will need to be typed. I like to start on that once I get a good start into my book--once I'm far enough along that I can look back at the start with a fresh perspective. Typing the manuscript into the computer gives me an excellent chance for a first round of editing. So the second binder is occupied by a printout of the typed manuscript.
Lastly, once you begin writing novels with much detail (and I never knew what detail was until I started writing my first fantasy novel!) you will generate a lot of miscellaneous paperwork related to your book; especially if you follow any of the tips I offer in the general fiction writing and character development sections. For a typical story you'll have character sketches for (at least!) your major characters, a continuation plan with notes you'll need later, maps of the locations you create, a timeline, and gobs of other things. For instance, one of the major themes in a story I'm working on now is change, so I have a "change summary sheet" that lists the ways all the major characters and some minor characters will change through the course of the story, and how that will affect the setting and the others. Each story will have its own specific set of paperwork associated with it. That is what I keep in the third binder.
I like to get the binders with a clear plastic front that you can slide paper behind, and make title sheets for each binder so I know quickly what's in them. If you get really ambitious you can make title sheets to go down the back of it too.