The most important part of polishing glass is to keep it wet. Dry glass may crack or break from the polishing friction. Traditionally, glass is polished with a grinding wheel and a mix of water and silicon carbide as the abrasive. Proceeding through finer abrasives wears away the rough edges. Fire and acid are also means to polish rough glass edges, but require more expertise. You can also simply polish by hand, using up to 400-grit sandpaper, water and your muscles.
Mix 100-grit silicon carbide abrasive with water to make a paste that will begin smoothing the rough surface. Insert your grinding wheel into the grinder. Wet your wheel and apply a bit of this mix to the surface.
Hold your glass to the wheel to grind and polish it.
Progress to 140-grit and then medium grits of 270 and 300. Clean the wheel completely between changes of grit mixture. Continue grinding the rough edges against this slurry on the wheel until they're smooth and whitish. The edge won't be clear at this point in the polishing.
Insert a diamond disc to the grinder. Polish the glass edge with a diamond disc once the rough edges are smoothed.
Use pumice and water with a cork grinding surface for the final finish.
Felt and and cerium oxide may also be used for the final finish. Movable grinding tools may also be used to polish. In this case, secure, wet and apply the paste to the glass, then polish with the movable tool. There are diamond hand pads that are flexible and used for hand polishing.
Wear safety goggles.