Did you register ADE with an AdobeID?
If not, you need to do so. You may need to de-register the current state (ctrl-shift-D, cmd-shift-D on Mac) and restart ADE before you get the chance to register the AdobeID.
You can only transfer books to an eReader if they are authorised with an AdobeID (or if they are not DRM books at all, in which case I suggest using Cabibre rather than ADE).
You register the AdobeID with ADE, this automatically registers the books with that ID when you download.
When yu plug in a eReader you get the chance to register the eReader with the same ID, and then you can push the books to the eReader.