I've been cleaning C&B pistols for many years with the following technique:
2 cleaning rods. One with a wool bore mop, the other with jag for dry or oil patch.
Tooth brush (one that your not planning to clean your teeth with
Water displacing oil of your choice...I use WD-40.
Dry patches (home-cut flannel is my choice)
Baby wipe(s)..
yes these are handy.
Water (hot, warm or cold, as available) plus a squirt or two of dishsoap. Put it in a washtub.
Remove cylinder(s). Place in water (water should cover).
Remove barrel from Colt-type revolvers.
Use baby-wipe to clean hammer, frame, cylinder pin, etc.
Dry and follow with oil.
Dip bore mop into solution (whist cylinders are soakin') and run through the barrel. rinse mop, repeat as needed.
Run dry patch.
Run oil patch.
Run dry patch to remove excess water displacer (oil), if needed / desired.
Use bore mop to clean chambers while submerged. This cleans the nipples at the same time.
Clean nipples with tooth-brush.
Remove from water, drain/dry (outdoors?..place in direct sun). Dry-patch chambers.
Apply oil generously and dry/drain/remove excess (I use an air compressor when available).
Grease cylinder pin.
Reassemble.
Cut patches to clean/dry/oil the cylider of a generous size (3"-4"diameter). This is a great aid.
Perform same operations to each pistol component back-to-back to minimize changing equipment and lost motion.
This is a science, right?...sorry I'm an engineer.
Also, for those mixing ballistol and water....might want to remember that water-soluable oils may not displace water as well as a true water displacing lube. Military CLP is a good lube/protectant.
Cleaning two revolvers of the same caliber requires less time than typing the procedure.
I use the same system when cleaning cartridge revolvers as well, but they are easier to dry the chambers.
I carry everything to clean/maintain all my firearms using two, small, nested wash-tubs. The "top' one carries all the gear, the bottom one is used for the magic cleaning solution.
Another handy item is a roll of toilet paper. It is the most efficient method for cleaning the BP shotgun I've tried.
Enjoy!
Slim