You should do this experiment on a bright sunny day. You'll need a thermometer, a box large enough to hold the thermometer (about as big as a shoe box), and some materials for the "roof", like white paper, black paper, aluminum foil, or anything else you want to try. You can decorate the box with a door and some windows to make it look more like a house, but the experiment will work even if you don't do this.
Put the thermometer in the box, then place the roofing material flat on top of the box. Check the temperature and write it down. Place the box in the sun for one hour, then record the temperature again. Try all the different materials. Keep an eye on the weather, because if the sun isn't equally strong for all the roof tests, your results might not be correct. Which type of roof resulted in the coolest house? What does this tell you about which roof would be best in the summer?
Now, before you go and paint your roof white, ask yourself some more questions - which type of roof would be best in the winter, when you want your house to be warm and toasty? What is the climate like where you live? Is it really cold in the winter? Is it really hot in the summer? How long does the cold weather last, and how long is the hot season? So, the answer to whether a white or shiny roof would help you save energy over a whole year depends a lot on where you live. That's the way it often is with suggestions about saving energy - there's no easy answer that works for everyone!