I remove the cylinder from the gun and the nipples from the cylinder. I put the nipples in a small cup with enough bp solvent (T/C No. 13, Ballistol, Butch's Bore Shine, Hoppe's No. 9 Plus, etc.) to cover them and let them soak while I clean and cry the cylinder. I use hot soap and water and a .45 cal cleaning jag on a pistol cleaning rod to clean the chambers and a tooth brush to scrub out the nipple recesses.
I thoroughly dry the cylinder and set it aside while clean the nipples. I run a pipe cleaner into the nipple openings and scrub the outside with a toothbrush. I dry the nipples, apply anti-seize grease to the threads and install the nipples.