While there are three ways to take a screenshot on your Samsung Galaxy Note 2, you cannot use the default Android feature, because it seems like Samsung disabled it. Fortunately you have some alternatives and you will definitely like on of the three ways of doing it.
You can either use the physical buttons, the S-Pen or just the display to do the screenshot and we will teach you how to do it in every way. I personally prefer to swipe my hand over the display, because it's quite huge, so it's the easiest way. This is my preferred method, because I don't always use the S-Pen and I also don't like stretching my fingers to press multiple physical buttons at the same time.
This is pretty easy and I am sure you will prefer it while using the S-Pen. Just press the S-Pen button while touching the screen and wait for about a second. The screenshot will popup and it will then appear in the notifications.
Hand swipe method
You can just swipe your hand from one side to the other of the display and it will be taken immediately. Just make sure to do the swiping fast, because otherwise you might just touch something on the display and the phone won't understand that you want to take a screenshot. You will shortly see it in the notifications area.
Physical button method
This seems the hardest method to me, for two reasons. You have to press the power and home buttons simultaneously and keep them pressed for 2 seconds. Though if you get it wrong, you might turn off the display or just go to homescreen, by mistake. I suggest you to try the other two methods, because neither me or my friends manage to get it right every time with this one.
After you take the screenshot, you will see it in the notifications area, where you can open, delete, edit or share it. It's pretty easy to do everything you want with it once you open the notifications area, as there you will have three dedicated buttons, thanks to Android Jelly Bean. Also if you tap the image, it will open in the gallery.