Fortunately,
@bsoccer, you have a hooked breech shotgun. It is simple to remove the wedge and ramrod the lift the barrels from the stock. I recommend removing the nipples so that when you put the breech of your shotgun into the cleaning solution which is almost any grease cutting dish washing soap and warm water. You will benefit by using a sturdy cleaning rod with a jag that fits the bore and grips the cleaning patch. You should have a nipple wrench to remove the nipples. Pyrodex fouling can be removed with soap and water and there is little danger of the dreaded Pyrodex rusting if the gun is cleaned, lubricated and protected.
My method is one of the many variations that are being used by members on the Forum.
So, for cleaning you need these materials, a bucket of warm water, a few squirts of dish washing soap, a cleaning rod, a jag and some cleaning patches to clean the bore. Remove the nipples and flush the breeches by pumping water through the breech with the rod and cleaning jag. Get both barrels clean. Dispose of the water. I use the water on the plants at home. Fill the bucket with clean water and flush the barrels again to remove residual salts and fouling. The water should be pretty clear by now. I like to use a couple of patches soaked with rubbing alcohol to displace residual water in the breech. Sure, WD40 works too, but rubbing alcohol is every bit as effective and cheaper. Dry the barrel with dry patches. An optional step would be to use a patch soaked with Ballistol. This seems to find fouling that somehow other may have been missed. Most often all the fouling has been removed, but I use the Ballistol patch anyway. The final step for the barrels is to protect the bore with a rust inhibiting lubricant such as Barricade or Boeshield. These dry with a thin layer of rust inhibitor to protect the bore.
You don't need to remove the locks to get them clean. With an old toothbrush and small rag, clean the locks with the soap and water. You have to be very thorough to get all the Pyrodex fouling removed. Wipe with an alcohol or WD40 wet patch to displace the water. At this time, I like to put a little bit of grease on the rubbing parts and the threads of the nipples before reinstalling them.
Assemble the shotgun and store the gun with muzzles down. Any moisture will drain from the breeches. In a day or two, run a cleaning patch with the rust inhibiting lubricant to catch any fouling that may be left and pulled out by your first pass with the lubricants.
A lot of good information can be found in this topic:
https://www.muzzleloadingforum.com/threads/tables-useful-information-thread-links.125795/
One topic missing however, is the topic on detailed cleaning of a muzzleloading firearm.
