Hold your phone in an upright position in your left hand with your thumb running along the left side of the device, your finger tips should be wrapped around the other side of the device if you are doing it correctly and the screen facing you (this bits important).
With your right hand(use the end of your index finger) activate the device by depressing the rounded rectangular plastic button on the top left of the device. Once you have done this you should look to the front of the device (be sure to wear protective glasses so you are not startled by the bright light). This bit is really tricky. Pay attention. Be sure that both of your eyes are open and you are facing the front of the device with nothing in-between your eyes and the device that may block your vision. If your network operators logo is displayed on the screen then your device is surely branded.
If you are still unsure, another test you may try is to take the phone in your right hand with the screen facing the palm of your hand. Look to the lower half of the devices back, if you see your network operators logo your device is surely branded.
If you are still unconvinced of the branding status of your device there is another test you could try. Place the phone back into your left hand as explained in the first method. By now the screen of your device has gone black. Don't worry you don't have to go through the laborious process of activating the device again, you can simply unlock it(which is much harder). Follow the steps at the beginning of this guide to depress the rounded rectangular button again, once you complete this process you only have moments to act. Quickly with your right index finger touch the screen on the curved bar, not letting go drag your finger off the bottom of the screen. Once you have mastered this you need to look for a triangular shaped button on the bottom left of the screen(it should be in a circle), using the index finger on your right hand lightly touch this symbol. Look for any icons of applications that you have not installed. If you see any demos that can not be uninstalled or a market with your network operators name on it then your device is surely branded.
If your device has passed all 3of these tests then you device is most probably unbranded.