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Choose the right rock. Wash the rock. Shape the rock. Rub the stone of rough grade sandpaper. Use fine grade sandpaper to remove scratches. Sand with 300 to 600 grade sandpaper. Rub the stone with a piece of leather with polish.
You can polish any stone you wish, but there are certain characteristics of a stone that will make it easier to polish. If you want an easy stone to polish, pick a somewhat softer stone like onyx, limestone or calcite. Stones that are very hard will take a much longer time to polish. However, though hard rocks take a long time to sand, they yield more shine than softer rocks.  To tell if a stone is soft, scratch it with another rock. If the scratch looks chalky, the stone is soft. Also try to pick a rock with a roundish shape, without major protrusions or indentations. If your rock is dirty, wash it thoroughly with soap and water. Use a scrub brush to remove any stubborn dirt or debris. After you are done washing the rock, pat it dry. If you want your rock to be rounder, use a small hammer or a chisel to chip away at the stone. Put on safety glasses to protect your eyes from chipped off rock, and wear safety gloves if you wish. Chip at any outcroppings or sections that jut out.  If you are happy with the shape of your rock, don’t worry about shaping it. You can also rub the stone over a slab of concrete to break off any protrusions. 50 grade is the roughest grade of sandpaper, and is great for further shaping your rock. Use the sandpaper on any protrusions or bumps in the rock you want to smooth. If you are happy with the overall shape of the rock, give the rock an even sanding with the 50 grade sandpaper to smooth it evenly. Take the stone and rub it with the 150 grade sandpaper. You may notice that the coarse 50 grade sandpaper left scratches in the rock; go over these scratches with the 150 grade sandpaper to smooth and erase these scratches. Do an overall sanding of the rock with sandpaper in a grade from 300 to 600. Focus particularly on any scratches in the rock. This grade of sandpaper is fine and won’t create scratches, but it can correct any scratches left by the sandpaper in other grades. After you are done sanding your rock, polish it using leather and tube polish. Purchase a tube of polish and a sheet of leather from a hardware store if you don’t already have them around the house. Then put a couple dabs of polish on the leather and rub the stone against it. This should give the stone a beautiful, lustrous shine. Make sure not to buy colored polish, or it may stain the stone.