There is a long thread about this at http://forums.adobe.com/thread/1098541
Basically, you need a reader app on the Nook. There is a probably a builtin one (?), if not install Bluefire reader app.
Use a file manager such as Windows Explorer to copy files from the PC (or Mac) to the Nook.
You can also probably install the Overdrive app on the Nook;
that should let you borrow, download and read library books on the Nook without going via the PC at all.
I put this in another post, I am not trying to spam. I have spent too much time frustrated with this ADE problem that I just want to make sure others get the message...
Here is a plan that works. I just did it on my Nook HD+. It requires a Dropbox account which is free and easy to set up.
1. Install Dropbox on your Nook HD.
2. On your computer or other device, put the .epub file for your book in a Dropbox folder.
3. Open the .epub file on your Nook HD.
4. Read and enjoy.
(It may prompt you to select which reader you want to use in step 3. Since I have the Books a Million reader on mine, it asked if I wanted to use that or the generic reader. Both worked to open the book.)
A couple other things...
Your Nook HD must be connected to the internet.
You can download the Dropbox app as a regular Android app in the Google Play Store on your Nook HD.
Once you have opened the .epub file, it appears as a regular book your Library on the Nook HD.
How do you get the epub, on the Overdrive library website, file from the NOOK into the dropox folder?
"On your computer or other device, put the .epub file for your book in a Dropbox folder"