There are a couple of different ways to take screenshots on Samsung's Galaxy devices, but the typical method is pressing the power lock button and home button at the same time. This takes the screenshot and automatically saves it to a folder in the gallery.
To take a screenshot on a Samsung Galaxy Note device with the S Pen, tap the screen with the S Pen for a couple of moments while pressing and holding the S Pen button. You'll see the screen flash and hear the capture notification sound. Once the screen's been captured, the image will appear with a toolbar of editing tools.
Using the editing tools, you can draw or write on the image with different pen tips, erase mistakes, and crop the image. When you're finished, tap the Done button to save it to the screenshot gallery.
I tested this S Pen method for taking screenshots on a Galaxy Note II and Galaxy Note 8.0, but it should also work with the Galaxy Note 10.1.