You need to authorize the Kobo as well as ADE (Digital Editions).
If the kobo is an ereader (not tablet), menu/Help/Authorize Device to ADE while the kobo is plugged in.
If you borrowed a book before authorizing ADE you won't be able to read it, or return it.
You must wait for the loan to expire and it will return itself.
You should be able to read on ADE and the kobo any books you borrow after authorization.