You've already been given good information and references. Only thing I would add is patience. Draw filing a barrel takes a great deal of time and effort. A man who knows how and has enough patience can machine a surface with a file VERY precisely. If you want to, you can even make a round barrel by draw filing.
Think of your file as a hand-operated milling machine and you will have a good start on the proper attitude. I haven't done a significant amount of draw-filing since about 1974 or so and that was on an aluminum work piece. I still know the procedure though.
Another item you will need is called a "file card". This is basically a wire brush with very short bristles that is used to clean the channels in the file. Don't try to do this with a bare file, get a properly sized handle for the file unless you like cuts and blisters. You should be able to find these items at any hardware store... same place you could buy the file. Bigger is better as well. The wider your file is, the more precise it will be generally. In theory, you could draw file a barrel with a three-cornered file a half inch on each side, but you will have a relatively uneven surface on your work piece.
Also, files are brittle. If you attempt to putt too much pressure against it, you can break it right over the pressure point. Easy does it. Plan to take at least a few months... or maybe a year.
As you are going for an octagon barrel, you want a combination square to check your angles. This is a relatively common tool and has both forty-five and ninety degree angles on it. I would suggest making the ninety degree surfaces first and then do the forty-five degree surfaces, but others might do it differently.
You
really need a good vise, one that is equipped with either aluminum or wooden jaws. These are easy to make from base materials. Don't try to clamp your work piece in un-padded steel jaws unless you want to spend hours filing out scratches you put in the work piece. I have heard of people who clamp the work piece on a work bench, but that seems a bit difficult to me.
If you got a concrete floor, put a rubber pad down. First, you will be spending a lot of time on that floor and your feet will appreciate the padding. Also, pretty good chance you will drop the file and/or the work piece. Either can be damaged by a concrete floor.
Once you have finished, I would appreciate reading about your experiences. I've got an octagon barrel that I am thinking about making into a half-round barrel with a "wedding band", and I don't have a lathe.