If you have a table of density values, you can look up the density for each. If you have actual samples of the elements, you can determine the mass of a sample and then see how much volume of liquid it would displace. For choosing the liquid, you need to make sure that the element is more dense than the liquid and that the element will not react with the liquid. For example, to determine the density of iron, you could take a sample of iron and use a balance to determine its mass. Then, place the piece of iron into a graduated cylinder with a known volume of water and measure the total volume of the water plus iron. Since iron doesn't react with water and it's more dense than water, this will work quite well. For other substances, such as sodium, you would need to use a different liquid as it reacts quite violently with water.
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Density= mass/volume. The two elements with the highest density are osmium and iridium. You could find this information on a periodic table. I attached a generator to calculate the density as well as an about page that details the highest density element. Refer to the links below.