The expansion is available via update 1.2, which can be downloaded via the update page on the Frictional Games website. As an added bonus, the update also includes a collection of five short stories written by Amnesia's main writer and illustrated by its concept artist.
Finally, Frictional has released the soundtrack to Amnesia. Those who pre-ordered or purchased Amnesia directly from Frictional can download the soundtrack for free. For everyone else, it's available for purchase from the Frictional store. We're not sure why you would want to listen to Amnesia's psyche-rending soundtrack outside of the game -- perhaps some people just like being on edge all the time.