With NOOK, you don't borrow library books through the NOOK App or through the device itself. You borrow the books via PC/Mac download which opens Adobe Digital Editions. Then you transfer the book via USB cord to the device.
The step by step instructions are in the link in my signature.
Library lending is eventually coming to Kindle and reportedly the books will download directly to the device.
Personally, I much prefer the NOOK app to the Kindle app, FWIW.
I'm weighing my options on the Nook vs. Kindle, and the Nook's main strength is the fact that I can borrow library books. Before I commit to either I wanted to check out the free Nook/Kindle apps on my Mac. I'm guessing the answer to this is no, but does anyone know if there is any way to borrow a book from a library with the Nook app without actually having a Nook yet?
Thanks in advance!
One other thing, in case it wasn't clear, you don't the Nook App to read the library books on the computer, you would use ADE, the same program used to download the library books and transfer them to the Nook.
Overdrive, the company that handles most library ebooks in the US, has an app for both the iPad and the iPod touch/iPhone that you can use for library books. You can also use any app that reads Adobe books such as Bluefire.