Cleaning a traditional muzzleloader is definitely NOT rocket science.
It is generally NOT recommended to remove the barrel on a longrifle. Repeatedly doing that will result in the pin holes getting worn and thereby the pins eventually working loose. Also when replacing the pins it is possible to get a little off center when driving the pin home and that can cause some wood removal. However, I do remove the barrel from my longrifles about once a year in late winter or early spring after hunting season is finished and give the rifle a through scrubbing and cleaning at that time. Otherwise, I will sometimes remove the barrel if I have been out in the rain and the rifle was soaked. In that case I need to dry under the barrel.

To remove the barrel, first take off the lock. There is usually two lock screws that pass completely through the stock, sometimes only one. Next, knock out the barrel pins. Use a proper size punch and always knock them out from the same side. A nail can work as a punch. Just, first, take a file and flatten the point Put the pins back in reverse order. Then remove the tang screw. Actually it doesn't matter whether you do the pins or the tang screw first. Often the tang screw goes through the stock and into the trigger plate. In which case, the trigger mechanism will drop out if the trigger guard is removed. After the pins and screws are removed, carefully just lift out the barrel. Sometimes it may stick, but slapping it with your hand should be all that is necessary to loosen it.

Everyone has their own preferred method of cleaning a muzzleloader. Myself, I have a small bottle of a mixture of water and dish soap. I just dampen a patch and run it down the bore, over and over and over again until the patches come out almost clean. If it is a percussion, I take out both the nipple and the clean-out screw at the end of the drum. I use a pipe cleaner to clean inside both nipple and drum. Then, I dampen a patch with rubbing alcohol and run that down the bore. I believe the alcohol helps replace the water. Next, dry patches, as many as needed. Finally, oil the bore. There are many products available for doing that. Just put some on a patch and run it down the bore. I use Bore Butter, but I know some others who don't like it. I use the same oily patch to then rub all around the hammer and lock, and the whole length of the barrel. Oh yeah, while the lock is off, give it a good scrubbing using an old toothbrush. Oil it lightly before re-installing it.
I use furniture polish, neat's-foot oil, or Marvel Mystery Oil on the wooden stocks, depending on the original finish. The Marvel oil has a red tint to it so I mostly use it on the cherry wood stock of my flintlock fowler.
i don't buy cleaning patches, either. My old t-shirts work just fine for cleaning guns of all types.
I've done it this way for over 40 years. It works for me.

Opps. I ment to say linseed oil, not neat's foot oil. I use neat's foot on leather.

Last edited by Rancocas; 03/12/21. Reason: opps - mis-statement