Here's my cleaning method and it has worked for me for many years. My guns are all like new with absolutely no rust and no residual fouling. Pristine bores.
If it is a percussion rifle, I remove the nipple and plug the hole with a small sharpened dowel. I then make a mixture of warm water (like you would use to wash your hands) and a small amount of dish soap which I pour into the bore with the gun standing on the butt. I let the water sit in the bore for a few minutes to soak everything loose. I then pour out the water and add some more and repeat. Doing this soaks loose all of the fouling in the breach area. When the water that I pour out looks pretty clean, it is time to remove the plug from the nipple hole and start wiping with wet patches. When the patches come out looking clean, I dry the bore with a few dry patches. At this point, there is still some residual moisture in the breach area that needs to come out. Spray some WD-40 down the bore until it starts to drip out of the nipple hole. This will remove all residual moisture. But, it is not a good protectant despite any claims to the contrary. So, you need to use some more dry patches to wipe out as much of the WD-40 as you can. Then, use a patch moistened with a good gun oil such as Birchwood-Casey's Barricade. Great stuff!
This takes care of the bore. You also need to clean your hammer face, the area around the hammer and any other place where you find any fouling. I also like to remove and clean my lock every time I clean my gun. To make this job as simple and quick as possible, I buy a can of spray automobile brake cleaner or carburetor cleaner. Both work quite well and dry quickely. Take your lock out of your rifle and take it outside and give it a good flushing with the spray cleaner. It will flush out all of ther dirt and crud and leave your lock sparkling clean but it will also strip away all lubrication from your lock. So, lightly oil the working parts. I say lightly because too much oil will attract dirt. Just a drop into the working parts is all you need. Then, wipe your lock with an oily patch to protect it from rust and you are ready to re-assemble your clean rifle. Wipe the outside with a light coat of Barricade to protect it and it is ready to put away. Unless you are going to put it into long time storage, you don't need any grease in or on it. Stuff like RIG is excellent stuff for long time protection but is messy to clean up and not needed for storage for periods of less than a year. Of course if you are in a tropical climate and do not have a climate controlled place to keep your gun, you may well benefit from using RIG and then spending the time to get it all off before going shooting the next time.
When you get ready to shoot your gun the next time, be sure to wipe it off, swab out the bore and fire a couple caps before loading it.
If your rifle is a flintlock, the cleaning procedure is the same except that you have no nipple to remove and you plug the touch hole with a small feather or toothpick. The area around the pan will require more cleaning than if you were shooting a caplock. A toothbrush is a handy thing to have when scrubbing this area. I have found that a Popsicle stick is awfully handy for scraping duties in this area. Do not use anything metal for scraping. Stick to wood or plastic for scraping duties when removing stuck on crud. Also a very important caveat is to never use a brass brush in the bore of your rifle. When it gets to the breach area and you try to pull it back out, the bristles will hold it fast and you may have a real problem on your hands. You can turn the brush clockwise to turn the bristles so that the brush will come out but it is best to just not use a brush and you will avoid the stuck brush problem. You don't need a brush anyway. Oh, BTW, if your rod tips are not cross pinned, do that right away so that you don't pull off your jag in the bore sometime. Not cross pinning is a mistake often made and it is a bad one. Cross pin those tips right now while you are thinking about it.