On a traditional rifle, if it has a hooked or button tang, then the wedge pin can be knocked out and the barrel comes off, out of the stock. Its then a matter of putting the breech end into a pail of water and pumping hot soapy water through it. This is done by dipping a patch in the water first. Lay the wet patch over the muzzle, push a cleaning jag on a ramrod though it, forcing it into the bore. Then work down the bore in short strokes to the breech. As you work that patch up and down it will pump water through the breech and even the drum and or bolster through the nipple port. Take the nipple off and keep changing patches until they come out clean.
Then I like to put alcohol on a patch and swab the bore with that. It will pull the hard fouling out if there is any. After that dry patch the bore with patches until nice and dry and clean. Then on a clean patch apply a quality gun oil, and swab the bore with that to protect the bore.
If the rifle has a pinned barrel like some of the Kentucky long rifles, and others.. you get a flush kit. Take the nipple or vent hole liner out, and then put the flush kit nipple in place of that. Feed the flush hose into a pail of water and follow the steps listed above..