desidog's 'towel' method is an alternative to the Laurel Mountain instructions and it does work well. It's a bit less labor intensive but takes longer.
The key to a good finish with the Plum Brown hot solution is to be sure to clean and degrease the barrel well. Very important - if you don't get it fully degreased (ie, de-oiled) it's almost impossible to correct later.
The key to the Laurel Mountain cold solution is to get and maintain, throughout the rusting period, a good high humidity environment.
And advice for both methods: take your time and be patient. Being in a hurry will almost guarantee sloppy results. The hot solution will take time to apply and you need to be sure the surface stays hot while applying, so set aside a good couple of hours; on the other hand you can start the next coat almost immediately after the first. The cold solution can be applied quickly, but the rusting period (3 hours) in high humidity should be strictly observed, so there's a long time between coats.
To apply Plum Brown I hang the parts on a wire and use a propane torch in one hand and the applicator in the other. Plan this out and practice using the applicator so the parts are stable and don't swing around. I spend a long time slowly heating the parts until a drop of water sizzles on the surface, and use the torch while applying to keep it uniformly hot. I've not found it necessary to plug the barrel to avoid rusting it but some folks recommend doing that - be careful not to let any of the browning solution into the barrel and you should be ok. If the Plum Brown result is streaky or uneven, no problem - just heat it up again and apply more. It blends well, unless, of course, the reason for the uneven surface is that you didn't take time to thoroughly clean/degrease, in which case you are SOL. You can get a good result in as little as 3 applications, but I'd advise planning to do 5 or so, just in case. The more you do, the darker it gets.
For the Laurel Mountain, I set up jigs to hold the parts on a sawhorse in the basement bathroom; it has a shower, so all I need to do to get a high humidity environment is to run the hot water in the shower a while and close the door, and if the steam dies down I just turn it back on again. Some folks build a humidity box out of plastic sewer pipe. You do want to plug the muzzle and touch hole/nipple hole to keep the interior of the barrel from taking up any rusting vapors from the solution. The first coat or two will look awful (uneven, splotchy, etc), but that will go away pretty quickly with additional coats. It takes at least 3, in my opinion, and I usually do 6-7 coats.