Summarize this article:

While you can cut harder gems, they'll take more time and effort to cut. Instead, choose gems that are lower on the Mohs hardness scale. For example, these softer stones will cut easily:  Fluorite Malachite Coral Pearl Amber To make a stable work surface, lay a cloth down. Set a cutting board on the cloth so the board doesn't slide around. Place a sheet of 180 grit sandpaper on the cutting board so the rough side faces up. Pour the water directly on the center of the sandpaper. The water will prevent the gem from becoming scratched as you smooth it. To create 1 smooth facet on the gem, hold it between your thumb and index finger. Firmly rub the gem back and forth across the area of sandpaper that has the water to smooth the surface. Turn the gem and rub it again to make another facet. Keep rubbing the gem to make several facets and roughly shape the gem. Once you've finished using the coarsest sandpaper, run a little water over the gem to rinse it of the grit. Remove the 180 grit sandpaper from the cutting board and lay down a piece of 400 grit sandpaper. Pour 3 to 4 tablespoons (45 to 60 ml) of water in the center of the sandpaper. Rub 1 facet of the gem back and forth to further smooth it. Repeat this for each facet of the gem. Consider rubbing the gem in circles occasionally to prevent grooves from forming. Pour a little water over the gem to remove the 400 grit. Remove the sandpaper and set down a sheet of 600 grit sandpaper. Pour 3 to 4 tablespoons (45 to 60 ml) of water onto the center of the sandpaper and rub each of the gem's facets across it. Remember to rinse the gem once you've finished with the 600 grit sandpaper. Replace the 600 grit sandpaper with a sheet of 1200 grit sandpaper. Pour 3 to 4 tablespoons (45 to 60 ml) of water onto the center of the 1200 grit sandpaper. Rub each facet of the gem back and forth across the sandpaper a few times. By now, the gem should be completely smooth on every side. Remove the 1200 grit sandpaper from the cutting board. Lay another cloth over the cutting board and tuck the ends under the bottom of the cutting board. Rinse the stone with water to remove any grit and dry it with a cloth. Squirt a dime-sized amount of liquid metal polish on the cloth that's over the cutting board. Take the dry gem and rub it vigorously through the polish on the cloth. Turn the gem and rub it again so that each facet becomes polished. If you're having a hard time seeing if the gem is polished enough, rinse it occasionally and dry it before rubbing it over the metal polish again. Run clean water over the gem to remove excess metal polish. Rub the gem dry with a clean cloth and examine it to see if it's as smooth as you like. Each facet of the gem should be smooth and shiny if you've polished it enough. If it still looks rough in spots, you can rub it over wet sandpaper again. Try the 1200 grit to smooth a small spot.

Summary:
Select a softer gem for cutting without a machine. Lay the 180 grit sandpaper and cutting board on a cloth. Pour 3 to 4 tablespoons (45 to 60 ml) of water on the sandpaper. Rub the gem against the wet 180 grit sandpaper. Rinse the gem and pour water over 400 grit sandpaper. Rub each facet of the gem over the 400 grit sandpaper. Rinse and rub the gem's facets over the 600 grit sandpaper. Finish rubbing the gem over 1200 grit sandpaper. Wrap the cutting board with cloth and rinse the stone. Put metal polish on the cloth and rub each facet of the stone against it. Rinse and dry the finished gem.