How can an author put the book online when the publisher owns the rights?

You will only be putting up an extract of your book (for readers to sample), not the whole book. This will allow potential readers to discover and "taste" your book. You are in total control of the pages (and the number of pages) that you want displayed.
Of course, you can and should inform your publishers about this, just to keep them in the loop. As you know, extracts are a critical part of the book marketing effort and publishers are aware of this, and hence typically have no objections. Further, the easy sharing option in BookBuzzr allows you to promote your book on Facebook, Twitter and MySpace.