While I prefer to do as Garrick suggested and keep my story in one big file,
some of my writing friends like to save each chapter as its own file.

Whether your on a Mac or windows machine.

Open a new folder.
Name it the title of your story.
Save all your story files into this folder so you can find them later.

If your borrowing someone else's machine and you don't want
them to see what your doing or save it there,
then open a free account at Yahoo or MSN mail.
Write your stories in the document of the e-mail and send them to yourself.
You can open e-mail folders in those accounts and file the e-mails
appropriately.

It just like having a folder with paper files in or on your desk.
Organization is key.

Good luck!