Color Vs. Fade Rate
One way in which you can study the effects of the sun is to see if there is a correlation between the color of paper and the rate at which it fades. You will need a dry place that gets good exposure to the sun. Select different colors of construction paper and place them in the sun to be exposed. Leave paper outside for two days, checking the sheets periodically to ensure they remain exposed. Keep one piece of each color you use inside and away from the sun, to be used as a control. At the end of the two-day period, bring the sheets inside and compare them to the control. Did one color fade more than another?
Types of Paper Vs. Fade Rate
You can also try the same experiment using different types of paper instead of different colors. Compare tissue paper, poster board, magazine paper and construction paper. Place the papers in the sun for two days, and check them after the end of the second day. Compare them to the controls to see if one type of paper faded more than the others, or if one kind fared better in the sun.
Control Your Variables
Be sure to eliminate any variables. In this case, since you will be placing the paper outside, try to find a way to minimize the effects of the other elements. Consider bringing the papers inside at night to avoid condensation on the paper. You will also want to shield the paper from the wind, if possible. Place rocks or other heavy objects at the corners of the papers to weight them down.
Logistics
Remember, these projects are weather dependent. Check your local weather report before beginning the experiment to make sure you will have two good days of clear weather with no rain. The sun's ultra violet rays cause a chemical reaction with the dyes in the paper, which is what causes it to fade. If you can, place the sheets of paper under glass or transparent plastic to protect them from the weather, but make sure it is not UV resistant. It is always a good practice to run the experiment at lease three times to control for anomalies and mistakes.