400 grit sandpaper to 800 grit to 1000 grit. Then a Dremel and extra fine polishing compound. There's a pretty good video on YouTube that shows how to remove the bluing off of the barrel using vinegar but I just used the sandpaper. If you start with too high grit sandpaper it doesn't remove the flaws in the metal so you have to step it up if you want a mirror finish.
I use sandpaper 400 grit to 800 grit to 1000 grit to 3000 grit. There is an excellent video on YouTube showing how to remove the bluing by soaking it in white vinegar but I just use sandpaper. I did a little polishing with a Dremmel afterwords also. It's my first time ever doing this and it came out really good.