This resource created by Phandroid.com Contributing Editor Kevin Krause as part of an Official Series of beginner tutorials for Android Forums.Chalk it up to seamless design, but it's totally understandable if you are having trouble figuring out how to remove the Note 4's back cover. Here's a pro tip: look for the little notch cut out of the rear cover just above the power on/off/standby button. Slip a fingernail in there (or the thin edge of something like a credit card, if you lack enough fingernail) and pry up.
Once you get the first corner up, work your way around the entire back gently prying it open. The seal might be a bit tight at first, but don't worry about breaking the back cover. It has plenty of flex. Once open you will have access to the SD card slot, SIM card, and removable battery.
To replace, realign the back cover and apply pressure evenly along the edges. When you hear the satisfying click you know the rear cover is now secure.