Here are some of my favorite settings for the Samsung Galaxy SIII,
I have upgraded to a Galaxy s4,
Oct 25, 2014 I got my Galaxy Note 4 I pre-ordered from Verizon.
1. Swipe down from the top of the phone to open the notification screen. Across the top of this screen are on/off icons for many of the features, for example to toggle Bluetooth, GPS, Sound, Screen rotation, Power saving, Airplane mode, Driving mode, Sync (you can scroll right to see the rest) you just hit the button. One button that I feel is missing here is the WiFi button (thanks to Verizion) that is on my other devices.
2. To change the rest of the settings including WiFi hit the little gear icon on the notification screen. You also hit the settings gear icon on your desktop (if you can find what screen you left it on), but I preferred to just swipe down to open the notification screen and then access settings from there.