After extensive firing I usually remove the grips and cylinder and run a couple of patches soaked in Hoppe's #9 through the bore followed by a few passed with a wet bore brush. Then I do the same with the each of the chambers. I let the solvent soak while I wipe the gun down with a clean rag with a little Hoppe's to remove exterior fouling. I try to get into all the nooks and crannies like under the cylinder star, around the area where the barrel comes through the frame, etc. A clean tooth brush helps with this. Finally, I wipe the exterior down with a clean rag, run a couple of patches through the bore and chambers and wipe the exterior with a clean soft cloth. A little lubricant like Breakfree CLP applied to wear points and a final wipe down with a silicone treated cloth complete the job. This is adequate for routine cleaning and short term storage. Any good commercial gun cleaning solvent is OK unless you have some special fouling problems.
I don't claim this is the "best" way, but it has worked well for about 50 years on a LOT of firearms!
