Deleting is easy but the process varies. Two questions:
What kind of Nook? Simple Touch, Nook Color, Nook Tablet, Nook HD, or the brand new Nook Glowlight?
What kind of book? Did you buy it from Barnes & Noble so it automatically downloaded on WiFi or did you "sideload" it (copy from your computer using the USB cable)?
On the backlit devices, there are a couple quick steps. Deleting is permanent, so be sure that's what you want to do. First, make sure you're connected to the internet. Next, press and hold on the icon of the book you desire to delete/archive/etc. A menu will pop up when you do this giving you several options, one of which is delete. You're good to go from there