To replace the battery in a Nook tablet, remove the back plastic paneling, find the side gaps, and pull the cover gently from the frame to reveal the battery inside a small, plastic panel. Remove the panel with a Philip's screw driver, and replace the battery with a new one.
To remove the old battery, place a finger in the crevasse next to the battery, and pop it from the frame. Insert the new battery into the slot, making sure the battery's terminals align with the Nook's. The Barnes & Noble logo on the battery should be visible. Screw the plastic panel back over the battery, and snap the plastic backing onto the tablet.