Fill the graduated cylinder partially with water to a level where you can submerge the object and drop the sinker weight into the water. If you don't have a graduated cylinder to fit your object, put a cylinder in a basin, fill it to the top with water and measure the overflow into the basin. Your answer will be less accurate because of the number of times the water has been moved. Note the amount of displacement in milliliters (ml) caused by the sinker and string.
Measure the mass of your object (say a cork) on a balance scale in grams (g). Be sure the object is dry when it is measured. Record its weight. Attach the sinker with the string to the object. If you use a staple or pin, be sure to include that when you measure the displacement of the sinker in step one.