The first time I clean a new gun (I usually do this before I ever fire the gun) I half-fill a five gallon bucket with warm water and dish soap. I remove the barrel from the gun, remove the nipple, and drop the nipple and the breech end of the barrel into the water. With a mop or tight-fitting patch I swab the barrel about 50 times, pumping lots of water into and out of the barrel. Then I scrub the nipple with a toothbrush, rinse it with clean hot water, blow through it a couple of times, and set it aside.
Then I dump the water from the bucket and refill with hot, soapless water. I repeat the swabbing until the barrel is hot to the touch. I blow through it from the muzzle, trying to blow as much water out as possible, then patch it dry with two or three patches. The heat in the barrel ensures that the last molecules of water quickly evaporate.
Then, using Bore Butter or Wonder Lube on a patch wrapped around a bore brush, I swab the bore a few dozen times. I put a bit of the same lube on the nipple threads and install it, then wipe down the outside of the barrel, along with the other exposed metal surfaces, with a bit more lube on a patch.
After that first cleaning, I never use soap, just clean hot water. The idea is that swabbing with the lube "seasons" the bore over time, making it more resistant to fouling and rust, and that soap tends to remove this "seasoning". I have no idea if this is true - and it sounds a little fishy to me - but by the same token, my guns are always easy to clean and never rust, even along my humid coast.