Tap the button in the upper right, and you get an expanded display of the quick setting buttons.
Now tap the edit button (looks like a pencil), and you get a screen that allows you to drag and drop buttons within and between two groups, those displayed by default and those displayed only in the expanded view.
Unfortunately, there is some bad news: the quick setting button to turn mobile data (3G/4G service) on or off has been removed. I went online and found various people complaining about this on phone company support forums. I can't blame them for complaining -- this is a feature I use fairly frequently when traveling -- but I think the complaints may be misplaced. I doubt that the service providers (Verizon, Sprint, etc.) had anything to do with eliminating the button. It's possible it was a decision by the hardware vendors (Samsung, did you do this to me?), but may also be a "feature" determined by Google.
The good news is in two parts. First, you can still turn mobile data on and off by going through the device settings menu, although it's buried fairly deeply. Second, there are free third party apps that provide alternative ways to toggle data service. One very nice one is Notification Toggle (henceforth "NT"). Once installed from Google Play, it will drop a launcher icon somewhere on one of your desktops, as seen in the next shot.
You'll also see an icon in the upper left corner of the notifications bar, telling you that NT is running. Tap the launcher to get to the NT home screen.
There are lots of things you can set in NT, but for our purposes the next step is to tap the icon to the left of the program name.
Now tap the Toggles menu item to get a list of built in buttons.
The number available is truly impressive. Scroll down a bit and you'll find one for "Mobile data". Put a check next to it. (You can see in the shot above that I also added a button to turn on flashlight mode from the notifications screen.) There's also a button labeled "4G", which I assume controls whether you use 4G when available or 3G only. Now go to any screen and swipe down to expand the notifications bar.
In addition to the usual stuff, you get some new buttons (circled in the screenshot above). The one on the left toggles flashlight mode; the one on the right toggles data service on (lit) or off (unlit, as in the shot above).