With a shotgun, I'll swab the barrel with a solvent soaked patch, then a solvent soaked brush, always from the chamber end. Then several dry patches until they come out dry and clean. Small amount of oil on a patch and swab the bore to lightly coat with oil. Then every 5-6 hunt/shoot/cleaning, I take down the gun to the barrel, action etc. by removing forend and all. You'll need to know how to do this without parts flying all over the room (not likely). Read your manual or go on line to get a detailed instruction on how to break down your gun. All of those internal parts, and ports need to be cleaned and oiled occationally too!
Wipe down exreior metal with oily swab, and I use Liquid Gold on the wood.