I found this.....He appears to be polishing by tumbling. But I think this still applys.
Polishing Obsidian- by Richard Friesen
Obsidian is a volcanic glass which often contains attractive colors and inclusions, but has a reputation as being difficult to polish, although it is fairly soft and is usually uniform in structure. When people are having problems polishing obsidian, I find it is almost always because they didn't get the sanding done adequately before attempting to polish.
Obsidian seems to show fine sanding scratches, especially the 600 grit ones, as a haze that won't polish out. A ten-power glass will usually show the problem, although many people won't see it until it is pointed out to them. More time on the 1200 grit wheel usually takes care of the problem. For best results I like to add some time using 3000 grit and then start to polish.
I have used cerium oxide and aluminum oxide to polish obsidian; both work. I like aluminum oxide better. For a real treat, polish a piece of obsidian with cerium oxide, then polish again with Reynolds* .2 micron polishing compound. When I've done this, I often have trouble finding the surface with a ten-power loupe.
