You didn't say if it is a Nook dedicated eReader or a Nook tablet.
In either case, you can't download Digital Editions (ADE) to it.
For an eReader you need to download ADE to a computer, and connect the eReader to the computer by USB.
It should then show up as a device on the left hand panel of ADE.
Some devices fail to show up in ADE2.0, in that case install the older but more reliable ADE1.7.2 (see below).
For a tablet, you need to install a compatible eReader app such as Bluefire or Aldiko.
Then copy the books using a file manager (e.g. Windows Explorer or Finder) to the drive the tablet should be mounted as.
Or maybe try the Overdrive app if you only want it for library books.
Overdrive can borrow and download library books with no need for a PC/Mac,
but quite a few people have problems with authorizing Overdrive on Android.
There are lots of bugs in ADE2.0. Try replacing ADE2.0 with the older but more reliable v1.7.2.
(You can have them both installed at once if you like.)
Version 1.7.2, it is a little difficult to find, available on Adobe site for Windows and for Mac.
The forum software is sometimes corrupting the link above. There shouldn't be a blank in 'editio ns.html'. The following redirects to the same page: http://tinyurl.com/diged172