here's what i do....
1)bust it down into the basic pieces-barrel, forend, rings (set down in the order and orientation they were taken off) and receiver.
2)swab the barrel with a copper brush covered with a rag covered with hoppes or something similar til the rags come out clean. Put a very light amount of CLP on another rag and pass it through the inside.
3.Wipe off the rings with CLP or if they are really grungy or got really wet, i like to Hoppes them first. Don't get the rubber o-ring soaked.
4.wipe off everything else with CLP. Unless you dropped it in the lake or something (duck hunting? yeah, it happens) then don't even worry about the magazine except maybe once a year.
YOU DON'T EVER WANT A LOT OF OIL ON YOUR SHOTGUN! or when it is 0degrees out, it will turn into a single shot autoloader....
Edited to add: steel wool on a shotgun??? *shudders* just use a flannel rag or something similar.