You're a good boyfriend!

What a great present!
You have to use a regular computer for library books. You need to have Adobe Digital Editions (most of the time referred to as ADE) to handle the library DRM (copy protection).
Check out the book from the library.
You'll be getting a ASCM file when you press the library's "download" button, but that's not the actual book, just a kind of link to donwload the book,
Open the acsm link and the book will be downloaded. If you've made "typical" ADE install the book will find it's way to there.
With ADE open, hook up the Nook with a USB chord and ADE should recognize it and you should be able to drag and drop the book to the Nook.
Once the book is on the Nook you will find it in the "My Documents" Library, not the B&N Library.