A) Cleaning a shotgun is a simple business. After using it, dismantle the gun into its main components: stock/action, barrels and fore-end. If the gun has got wet, dry it thoroughly using kitchen paper. It is always a good idea to dry the barrels using a gentle heat source such as a radiator or the back of a range.
Next, scrunch up a piece of newspaper or kitchen roll and push it through the barrels with your cleaning rod. Make sure it is a tight fit so that it will remove all the loose powder fouling and any other foreign matter. If there are any traces of lead or plastic from the wadding it will show as a grey smear. This can be removed with a phosphor bronze brush. Pass more kitchen roll through the barrels until it emerges clean and then oil it using the woolly mop in the cleaning kit. I like 3-IN-ONE oil, but any light machine oil will do. Next, clean the action, using a small paintbrush. Pay particular attention to the lugs and their corresponding slots. Remove all dirt and grit. Any mud on the stock can be removed with a damp rag. If there is mud in the chequering, remove it with a worn toothbrush.
When you are satisfied that the exterior of the gun is clean, reassemble it. It should then be treated to prevent rust. I prefer a silicon or hard wax polish finish as it does not attract dust in the same way as oil. Be sparing with oil if you use it and avoid getting it on the stock, as wood does not react well to mineral oils. Store the gun barrels down to avoid any oil leaking into the stock. Check the gun periodically to ensure it has not rusted.