I usually use a clear vinyl tubing assembly with a rubber O-ring that clamps around the touch hole. I drop the weighted end of the tube in a small container holding warm water. I then scrub the barrel with a wet patch on a cleaning jag. On the up-stroke, the wet patch creates suction that draws the water up the tube and into the barrel. On the down-stroke, water is pushed back out. I alternate repetitions of using the wet patch and brass brush, changing the water a couple of times until my patches are clean. I then dry the barrel with patches, paying particular attention to pumping them near the breach to blow water out of the touch hole. (My guns have something of a patent breach, which is hard to access.)
After that, I lube/protect the bore. If I won't be shooting for a while, my strong preference is to use Break Free CLP. It's an excellent protectant that won't create a glaze or gum over time. Also, if I wasn't thorough enough with my warm water routine, my Break Free patches will remove it (and clearly show it). However, if I'm cleaning during hunting season, when I don't want to worry about getting all of the oil out of the bore before loading again, I lube with Lube 103, which is something along the lines of chap stick in consistency. I can simply load and shoot the next time out, with no barrel wiping needed. The Lube 103 is also a good patch lube and is perfectly adequate for storing guns for several weeks, but Break Free is much better for longer periods.
To clean the lock, I drop it in a container of warm water and clean with q-tips and patches. I shake, pat, and blow it dry, then lube also with Break Free, trying to avoid getting it in the flash pan. I also shake, pat, and blow excess oil off, then reassemble the lock onto the gun.
