Put your trash samples into airtight containers and cover each with dirt from the outdoors. To test different types of substances, include a paper towel, a banana peel and a plastic bottle. Make sure the items in each container are completely covered with soil.
Aerate the contents of the container by turning the soil and sample over inside the container once every day or two. Exposing more surface of your trash to the air will expedite the decay. Similarly, those who compost their organic trash are encouraged to aerate their piles by turning the contents over. This also helps to reduce odor.
Notice how the pressure in the airtight container builds. If you're using a plastic bag, you'll see the bag begin to swell as the microbes in the soil start to break down the samples. If your sample is in a container, you'll hear a popping sound when you open the lid, and the walls and top will be firmer to the touch than before the reaction began.
Notice and record how long it takes for your sample to disappear. The fastest items to decompose will be food; vegetables can vanish in as little as a week. Newspaper can take at least two months. Over the short timeframe of a science project, you likely won't see any change in plastic.