I run a brass bore brush down the barrel multiple times. Then dip a shotgun patch in solvent; wrap that a round a nylon bore brush and scrub the barrel multiple times. I remove the patch get a new patch and do again after sitting for several minutes I get a clean patch and run it down the barrel. I get a new patch every time until it comes out clean. Then I get a patch with denatured alcohol wrap it around the nylon brush and scrub the barrel. Then I use a hair dryer to ensure the alcohol dries out of the barrel or if I'm not going to hunt immidiately I let it air dry.
This is what I do after every shot. It's a lot of work but if I'm consistent my patterns typically are as well.