Do some research on the topic. In the introduction to your project you will want to include some information on why you chose this topic and why it is relevant to our lives and desires to be more "green." Conduct research using books, the Internet, textbooks and interviews to answer the following questions: How long does it take a plastic bag to break down in a landfill? What is the cost in terms of materials and labor to create a plastic bag? What does it mean if a plastic bag is labeled "biodegradable"? What is the cost of producing a cloth bag? How much does it cost to purchase a cloth bag?
Interview a manager at your neighborhood grocery store to find out how much it costs to purchase each plastic bag. Obviously, the plastic bags will cost a tiny fraction of what the cloth bags will cost. In the write-up for your science project include the reasoning other than cost (such as environmental friendliness, longevity, strength, size) behind considering cloth bags as an alternative to plastic.
Consider the strength of each bag. Fill the bags with heavier grocery items: 2-liter bottles of soda, gallons of milk and large cans. Compare how much each can hold before the bag rips or the handles break. You may want to conduct this experiment using items to stand in for the heavier groceries, such as bricks, so you do not ruin the food items.
Compare how much can be held in a typical grocery store plastic bag. Fill plastic bags with typical grocery items -- such as bread, eggs, milk -- and compare which bag holds more, the plastic or the cloth. Keep track of the average number of items each bag can hold and record those averages in your data chart.