Before you update, assuming your iOS device is supported, make sure you’re running the latest version of iTunes (11.1 for OS X Mountain Lion) by launching iTunes and going to the iTunes menu and choosing Check For Updates…. . Alternatively, you can download iTunes from Apple. Then, connect your iOS device to your computer with the USB cable, and backup your device to your computer.
Once you’ve updated and backed up, connect your device to a power source, go to the Settings App, then General, then Software Update to update your device.
After the iOS update arrives, update any apps that need it, then read this excellent TidBITS article by Tonya Engst: iOS 7 Pre-flight Checklist.