Wipe barrels through with tissue paper to remove dirt and loose debris.
Couple of drops of Young's 303 in each barrel and pass through/spread with brass Payne Gallwey brush. (Addition if they have been wet, place barrels on warm radiator until totally dry.)
Leave at least 10 minutes - meanwhile, drop of Youngs 303 on finger and clean residue off action face and around firing pins.
Further scrub with brush, then tissue paper though until clean(ish) (about 3 or 4 times).
Check clean and free from leading streaks - and if not repeat. Bores should be near mirror bright.
Spread a couple of drops of oil in each barrel with fibre Payne Gallwey brush
Clean under ejectors with oily cloth - if necessary take out, clean and lightly grease (about twice a year)
Tissue off old grease from hinge, lumps, knuckle etc - and small smear of fresh grease (any general purpose grease)
Reassemble. Wipe external metalwork with cloth and a drop or two of Rangoon oil.
About once or twice a year a little stock oil (Phillips walnut oil).
Important points;
Use the opportunity to check over carefully for corrosion, damage etc.
Clean off old oil and grease taking dirt and grit with it.
Fresh oil/grease should be very sparingly applied so that it NEVER runs down.
Finally, two things that don't go near my guns (in normal cleaning anyway) - WD40 and wirewool.
