Are lots of ways to clean one...and lots of new products to try...but I've relied on hot water and soap for the 35 years I've been shooting them with no problem. The only neww addition to the cleaning system has been to use a little Murphy's Oil Soap or Simple Green.
This looks long, but it takes 10min. to do.
Cylinder out, frame open.
Hotest water you can get from the tap into a container. Add a bit of Simple Green or Murphy's Oil Soap (about a 10:1 mix). Drop cylinder into the solution and scrub inside of frame with toothbrush dipped in the solution while the cylinder soakes. Scrub the barrel with wet patches of the solution (can use a brush if yu've the urge). Scrub the hammer face and slot in the frame for the hammer with the wet toothbursh...lots of fouling seems to colect here. Give the cylinder pin a good scrubing while you are at it. Set the barrled frame aside (but not in the solution).
Then tackel the cylinder (it wil be the most filthy). Fish it out of the soultion and scrub the outside, exp. around the nipples. Remove nipples and let them sit in the container of solution. Scrub each chamber as you did the barrel. Scrub the center pin hole as you would one of the chambers. Tooth brush the nipple seats on the cylinder. Q-tip the nipple threads in the cylinder.
Dump cylinder back into hot solution and fish out the six nipples. Scrub each with the toothbrush..then work one or two bristles of the brush into the nipple's vent. IF cool enough, BLOW through them. Drop them back into the solution.
Dump solution (careful not to dump the little nipples too)...stick the container under the tap and turn on the hot water...rince all the metal parts in hot water, fish them out, and set them on paper to dry.
Run hot water through barrel...can either just put it under the tap or pour it through with a funnel...or a funnel and a rubber hose.. Set it aside on the paper to dry.
Pick up each pice as it dries and shake it...blwoing out with compressed air is nice, but most dont have a compressor...so if the water seems to wat to collect in hollows, just pick the part up and shike it to fling the water out. Once dry (and if thw water was hot, it will dry fast), re grease the center pin, coat the parts with a preservative oil,reasseemble, and put it away.
Make amental note to check on it a day or two later.
That's it...sounds like a lot, but it takes all of 10min. once you get use to it.