At our club we do many things, including TUMBLING. we have a rotary tumbler which is set to be going most weeks. This takes the rough or semi rough stones, and rotates them in a drum, with Grit (corundum) and water. This process wears down the sharp edges. This is done with various stages of grit (hardnesses or coarseness) until we get to a pre-polish and then final polish powder, which normally we would use a powder called tin oxide, or even aluminium oxide. This will give the stones their final shine (polish). The whole process usually can take from 4 to 6 weeks, depending on the hardness of the stones.
We at the club use the MOHS SCALE OF HARDNESS. This shows us the hardness of various stones, with TALC being the softest, and Diamond being the hardest.