What adobe do I need to download books from public library to my nook. Do I have to pay for this? I can't seem to get it. It says I need an unlock code?

OK.  You have downloaded and installed ADE on your computer right?  What operating system and version of ADE is it?  Start ADE, go to your library web and "check out" a book.  You should be offered an ascm file.  Click run and the book should download to ADE.  At this point you should be able to read it on your computer.  You should be able to authorise your Nook from ADE and transfer the book to the Nook.  If you are getting a request for a password maybe your library can advise a solution.