Google has been scanning in books from public libraries and other sources for years. It's something that has gotten them into a bit of a legal pickle in some cases, but they still have a huge collection of books that are out of copyright, and that means you've got access to an entire library of classic literature that you can read on the computer or on a variety of mobile devices and eBook readers.
The first step is to go to make sure you're logged into your Google Account and go to Google Books at books.google.com.
You may be used to the old Google Book Search, which was primarily used for research. Their search engine would search through their library of books and provide you with anything from a snippet to an entire book, depending on the book's copyright status and Google's agreement with publishers. You can still use Google Books that way, but in this case we want to read the entire book, so we're going to choose to go to the Google eBookstore by clicking the appropriate button.
You can also skip the button and get there directly by going to books.google.com/ebooks.