This is the process I have used for over 40 years.

Remove the lock and run it under the tap with water that is as hot as it can come out. Scrub with a tooth brush to get in the tight areas. The hot water will heat the metal so that it will dry faster. When dry, spray the entire lock with WD40 or Break Free CLP and let drain on a paper towel. Next, put a round tooth pick in the touch hole of the barrel to seal it and pour some black powder solvent down the barrel. (I have an old mustard squeeze bottle I use and I like Track of the Wolf's brand bore cleaner but even just Simple Green cleaner works fine and is cheaper.) Squirt some cleaner down the barrel and with your finger over the muzzle, flip the gun up and down to slosh the solvent back and forth through the barrel. Pour it out and repeat until it runs clear, usually about 2-3 times. Now lay the gun horizontal with the touch hole facing down, pull the tooth pick and run several patches wetted with solvent through the bore. Excess solvent will squirt out the touch hole so by placing the gun horizontally, it will not run down the stock. Follow up with dry patches then oil the bore with any good gun oil. I use the Break Free CLP. I also oil the exterior of the barrel with the oily patch and clean any powder residue off the stock with it. The stock can be waxed with a good paste wax to help preserve and waterproof it but just wiping it down with the last oily patch works well too. Put the lock back in and you're done. Takes about 15-20 minutes.

The same process works with percussion guns as well if they don't have a hook breech system. I remove the nipple and clean it under hot tap water. When dry, apply white lithium grease on the threads, set aside. I then screw in a bolt matched to the thread size to seal the breech. Clean the bore as detailed above. By cleaning the threads of the nipple each time it keeps it from rusting in place making it difficult to replace. It will also keep fouling from building up in the threads and corroding them which can cause the nipple to become lose and blow out. You can also check it for wear or broken threads. Replace it if anything looks worn.  Be careful when reinstalling the nipple not to cross thread it. Replacing the nipple is cheap compared to having one blow out. The nipple, and often the top of the hammer, will become a projectile headed for your head or anyone next to you.