I have inletted about 130 barrels by hand since the 1970's. The first dozen or so were slow and tedious, sometimes taking weeks, mainly because at the time, all I had was a 1/4 inch chisel and a rawhide mallet to do the job. There is a slow learning curve on this. I think Mark makes an excellent point, the only way to learn is to make mistakes. It does take a few different hand tools to speed up the job.
The way I tackle it is to first draw the barrel profile on top of the stock with the plug removed and then, using a large # 9 gouge hog out the wood inside those lines, pretty much to final depth. Then, when you lay the barrel into your rough mortise, your barrel side flats should be very close to the top surface. Then, draw the outline with a sharp razor knife, remove the barrel and go over those lines a few times with the same razor knife. Don't try using a pencil it will not be precise enough. Using this line and using a wide chisel, cut straight down to establish your side flats. Obviously for a round barrel you would not perform that step.Then you can start using your inletting black, candle smoke or whatever to finish fit. I find that a variety of dogleg chisels (bought at flea markets and reshaped) help greatly as well a few skew chisels.
With practice, the procedure can go quickly, I completed a 46 inch, oct to round barrel this weekend, in a piece of nice hard curly maple, I had about 4 and half hours in it to complete. I recently had a project with a 38 inch, straight barrel, in the hardest, curliest, most cussed piece of maple I have ever seen and it took over 15 hours as it was impossible to make more than tiny shaving cuts at any time to avoid any tear out. It would have been easier to inlet the barrel into the concrete floor of my shop. But it will be a spectacular piece of wood when done, the customer had been hanging on to it for over 40 years. It is nice and stable for sure.
I don't find that straight barrels are any easier that swamped or oct/round, the process is pretty much identical.