In chemistry, specific gravity is a density comparison. Solids and liquids are compared with the density of 'pure' water at 293 K, while gases are compared with hydrogen at the same temperature.
This is a comparison. The substances you're using must be comparable. What you have to have is water and (your favorite substance) at the same temperature and pressure in order to compare them. First you find the density (mass/Volume) of one, then the other. Then you divide: (your favorite density)/(density of water). It's best if the common temperature that you use is somewhere near 293 K = 20o C, because water changes density in a really funky way as it's temperature changes. That's why they don't use water for thermometers...
Osmium and Iridium are my favorites, because they're the densest elements. Osmium has a specific gravity of 22.4, while Iridium's is 22.5. For interest's sake, suppose a cubic foot of water weighs 64 pounds. Then a cubic foot of Osmium would weigh about 1430 pounds, and the same amount of Iridium would weigh 1440 pounds. Put another way, a Rubic's cube made of either substance would weigh nearly seven pounds.
I found this data in one of my dad's old chemistry books, and added to it some information from http://chemicalelements.com/ and Webster 2002.