You can grab it on Steam or the official site. Steam is offering a 10% discount on the DLC, reducing it to $4.49, but the official site offers a "Complete" version with the DLC and soundtrack. Choices.
Klei noted in the announcement that a PlayStation 4 version of Reign of Giants is in the works too, and details on a release date are forthcoming. For now, check out a new trailer.
Steve Watts posted a new article, Don't Starve 'Reign of Giants' expansion released.
Don't Starve's Reign of Giants expansion has released. It's available for $5 and adds lumbering giants, along with new characters, seasons, and items.