There are 2 methods of doing this. One being the default where you press a combination of keys and the other is a bit more fancy.
- Go to the place of which you want to take a screenshot of (it could be you homescreen, a settings menu, an app, etc).
- Now begin to hold the Home button and the Power button together for atleast a second or two and release them. It's important to press the two buttons simultaneously otherwise it won't work.
- You should see a screenshot effect of your screen (white border lines) aswell as a notification in your statusbar.
- Head over to the Settings of your Galaxy S4
- On the top, tap on where it says "My Device".
- Look for and go to "Motions and gestures".
- Now turn on "Palm motion" and go there.
- Make sure "Capture screen" is turned on.
- Now simply swipe your hand from the left side to the right side of your screen and you should hear and see the same results as in method #1.