Find two small, identical containers, such as polystyrene or plastic cups, and, using the sharpened tip of a pencil, poke four small drainage holes in the bottom of each one. Label one cup "L" and the other "D" for light and dark and fill two-thirds of each container with the same type of planting soil. Weigh each cup and adjust the soil levels until the two are identical. Take two pairs of runner bean seeds and plant two seeds roughly 1/2 inch beneath the soil's surface. Provide each plant with a controlled amount of water. Take a photograph prior to placing the cups in their controlled environment so you can demonstrate that you controlled the variables.
Find a pitch black environment where your dark condition plant can go undisturbed and will be kept at a stable, room temperature. Consider placing a large plastic bucket upside down over the dark condition plant to ensure that your plant will not be accidentally exposed to light. Locate a brightly lit room at room temperature where you can keep your light condition plant. Place your plant on a windowsill, so it receives a plentiful supply of natural light from the sun. Leave a note next to each of your plants explaining the experiment to lessen the chance that they are moved or disturbed.
Check on your plants at least once every other day. Make observations about their growth levels, including the height and span of the plants, number of beans growing and the general efficacy and healthiness of the plant. Take photographs of your plants showing the experiment set up and size of the plant; to add to this effect, stand a ruler next to the plant and take the photograph so you can show its height in centimeters. After you have made your observations, give your plants a medicine dropper of tap water. Continue your experiment and observations for at least three weeks, so plants have fully germinated and grown to a decent size.
Your science fair display should include graphs and photos as well as a detailed explanation of photosynthesis and how your experiment demonstrates that plants need light to grow. A pair of graphs you can generate relate to the measurements for plant height and width that you have taken during your observations. Use a light colored line for the light condition plant and a dark colored line for the dark condition and plot a graph with time on the horizontal axis and height on the vertical axis. Create a second graph displaying plant width on the vertical axis.