Instead of just reciting the steps to get what you're looking for (if you're in a hurry, skip to the slideshow below), perhaps it's a good time to learn a bit more about your device and what an Android "launcher" is. Basically, your launcher is the application that gives you your homescreen, your app drawer, and even your settings menu – from the way they function, down to the way those look. All major manufacturers have their own launchers on their devices (that is, they're different from the stock launcher provided with "stock" Android developed by Google – it's been modified), and that's why a Samsung device has a markedly different interface than an HTC one.
As you can imagine, launchers also dictate how wallpapers are handled. Some launchers, like the ones on the LG G3 and the Sony Xperia Z3, allow you to not just change your wallpaper, but also make it scrolling. In other words, the background image will move along as you swipe left or right through your home screens (the one you're introduced to when you unlock the device). It's a cool effect, but not all launchers support it – for example, you can't get a scrolling wallpaper on your HTC One M8 or Samsung Galaxy S5. If you really dig scrolling wallpapers, though, you can simply download a third-party launcher off the Google Play Store – a few very worthy examples can be found here.
That concludes our quick lesson on Android launchers. Still wanting to change that ol' wallpaper of yours? Head right into the gallery, then!