First you need to be certain that the gun is not loaded. Recheck the barrel so that you are sure the shell or bullet is not there. If there are any magazines inside, remove them. On the cleaning rod, put the cleaning patch. Put some powder solvent on the patch and clean the barrel of the gun. Check the patch to see signs of residue or dirt. Change the patch if the previous one is dirty and repeat the process. Keep doing this until the patch comes out clean and discard the dirty patches.
Modern chemicals may damage some sensitive parts like muzzle loaders, clean them with hot water. Loosen the screw and remove the barrel. Put the barrel in the bucket and pour hot water over it. With the help of a clean patch, remove the dirt. Change the water after it gets dirty. Clean the barrel with a new patch after this. Remove the water and let the barrel dry. You will need to fully dry it with some more patches.
Lubricate the barrel with some gun oil and then clean it again with water. Apply the oil with a clean patch and rub it on the barrel. With the help of a brush, remove any stubborn deposits that do not come off with a patch. The gun oil should be applied to all exposed parts: levers, bolts and firing pins. Wipe it with a clean cloth after words. This will remove corrosion from the surface and also remove any finger prints.
Lastly remove dirt and grease from the wood stock of the gun. A soft cloth and a soapy solution will work well here. Do not perform any repairs as it can affect the authenticity of the gun. The fading colour is a sign of a good vintage gun.