For my shotguns, I tear them down and clean/flush the action and trigger group with Rem Action Cleaner (I now see it called Shotgun Cleaner too). I then use some Rem Oil and swab the bore. I then take a Brass wire brush and cleaning rod, and stick into the end of a drill. I then clean the barrel and choke tubes with the drill/brush. This will get rid of every bit of fouling in the barrel. I then re-swab with oil until the patches are clean, and assemble. I then put final coat of Barricade/Sheath on all metal surfaces.

For rifles, I like using Gunslick Foaming bore cleaner. I like this product because it has no strong amonia odor. I foam the barrel and rest the gun upside down on a rag for half hour or so (until the foam disappears). This will eat up the copper fouling, the rag will turn blue/purple. I then run a nylon brush through the barrel, and then a jag/patch with rem oil through the barrel. This will remove a substantial amount of copper and powder fouling (the patch will be blue/black). I reswab until the patch comes out clean. I remove the stock, and then apply a coat of sheath/barricade on metal surfaces.

One word of caution, you should not use Gunslick foaming bore cleaner on gas operated semi-autos.