Want to see a writer scream? Turn off his computer without letting him save his files. Computers crash, electricity goes out, and people make stupid mistakes. No matter how your work in progress disappears, nothing beats that sinking feeling when you realize your hours of work are gone and there's no way to get them back. Backing up your work allows you to store multiple copies of your book in various spots, to ensure that you'll always have access to your work. Always use one or more of these methods every time you quit writing for the day. 
Computer Files
The simplest way to back up your work is to make multiple files on your computer. No matter where you write, whether it's Word, Open Office, or one of the dedicated writing programs, it will have a way to save your work in a file. An authors first line of defense, when it comes to locking away your work, is to create a separate file somewhere else on your computer. Create an empty file in your documents folder, then send a copy of the work to that folder. If your writing program gets corrupted, you'll have a clean copy of your manuscript to carry on with.
Flash Drive
These tiny storage units plug into your USB port, creating a new file on your computer desktop. Once you save your file for the day, drag a copy of the work onto the flash drive. Save the file in the drive and remove the drive from your computer. You've got a fresh copy, completely separate from your machine. Flash drives come in convenient keychains, wristbands, and dozens of shapes and colors, which are all simple to store.
Cloud Storage
You store your blog online, if you use Gmail your email's online, why not store your manuscript online, as well? Cloud storage sites give you the ability to store megabites of information in a locked file, accessible to only you or any designated individuals you might name. Simple sites like Dropbox give you the ability to drag and drop files into an icon, which transfers them instantly into cloud storage. Access your work anywhere, on any computer, by logging onto the site.
One very old school method of saving your work can be ideal for chapters, short stories, and smaller pieces of work. Copy and paste the words onto an email form and mail it to yourself on another email address, or send it to someone else for safekeeping. This is one of the earliest forms of ensuring that words online don't disappear, and has survived because of its simplicity and ease of use. As long as you or your chosen recipient don't delete the email, the words will stay safe for years.
Keep the Faith and May the Force be With You!
