The S4 has 2 built in ways to mute or stop notifications or ringtones.
#1 Go to settings>my device>motions and gestures>motions and press on the description which will bring up the motions menu. Slide the slider at the top right to on, then turn on the last item, "Mute/pause". With that set you can simply turn your phone over when it rings to silence it.
#2 Similarly, in the motions and gestures menu, you can select palm motion (press the description to see what's available), slide the slider at the top right to on, then select/turn on mute/pause which will allow you to simply cover your phone with your hand to silence the phone.
And since you have one of the best phones available, play around and check out all the other cool stuff it can do.
Have fun!