Step 4: Finishing the Edges
Professionals who do this for a living will "flame roll" the edges of the glass making them shiny and smooth like a standard glass. Unfortunately that requires specialized tools and you'll want to carefully anneal the glasses afterwards to minimize the chances of cracking and breaking.
** You cannot simply take a propane blow torch and get the edge smooth! If you try it, it will simply crack the whole glass. If you really want to do that, you'll likely need a glass worker's torch (usually Oxygen/Propane).
Using a Dremel tool, I first rough up the sharp cut using a Silicon Carbide conical grinding tip. Oh yeah, wear a dust mask, you don't want to be breathing ground glass!
Roughly grind the inside and outside of the edges using the Dremel. I also placed a strip of aluminum tape around the rim of the glass so that my grinding comes out as even as possible.
Continue to smooth out the edge using drum sanding attachments: I used 80, 120 and 150 grit. I would have used finer grits but that is all that I could find for the Dremel.
After a while, you'll have a fairly smooth edge that although usable, it is still kind of rough. Time to sand by hand using 200 grit sandpaper or finer.
You can keep going with a finer and finer grit, but if you want to finish the glass sometime this year, you'll call it a day after 200 grit.
You can also use a wire wheel on the lip, you'll get a shiny silver edge on glass that actually looks pretty cool.