Download online software developed for book writing. Fastpencil (www.fastpencil.com) offers a comprehensive alternative to a traditional offline word processor. It allows you not only to write your book using its software, but has also partnered with Barnes & Noble for self-publishing once you are done. Google powers Google Docs (docs.google.com) which allows you to use preset templates to create PDF documents of your masterpiece.
Determine whether or not your book will be published as you write or after it is complete. If you wish to share your story with the world as you go along, you may elect to join certain communities where you can publish your book in chapters; thereby, getting instant feedback on what you've written. Websites such as WEbook (www.webook.com) offer a PagetoFame program where, for a nominal fee, you can submit your works in progress for instant feedback as you write.
Sign up for a blog. An easy and inexpensive way to write a book online is through a blog service. This will also give your book public exposure, or not, based on your own blog settings, which can encourage readership as you go along. Blog sites like Blogger (blogger.com) and Wordpress (wordpress.org) offer printing services through Blog2Print (blog2print.sharedbook.com), to give you a hard copy of your book upon completion.