When cleaning the bore with a conventional cleaning rod, you push it through the muzzle. Use a bore guide and/or be careful when doing this, as you don't want to jam the rod against the rifling at the muzzle. The chambers are cleaned through the rear. You can also use a flexible "Bore Snake" device. The front face of the cylinder and rear of the barrel will build up carbon, and the area under the extractor star must be kept clean as well. Every so often (say every couple of years) you may want to remove the sideplate of the frame and flush out accumulated lube and carbon. This is not as easy as it might appear.
Any moving parts should have a light coat of lubrication, preferably with a lube designed for firearms. I like Break-Free CLP in the small squeeze bottle with a nozzle tip, myself. Swing the cylinder out and put a drop on the cylinder hand (through a slot in the rear of the frame). I also like to cock the hammer and put a drop on each side of it, but this revolver has no exposed hammer. The lube will eventually work its way in to the rest of the parts. The front tip of the ejector rod and and where the cylinder turns on the crane need a drop each.
