I take a lead away cloth and cut a small square and run it through the barrel several times. I then take Gunzilla and run a saturated patch through it several times. What also works best is that you saturate the bore and area between the top strap and forcing cone and let it sit overnight. The next day run another patch through the bore. Overnight allows the solvent to work at breaking up the fouling. For the area between the top strap and forcing cone a poster suggested using an old shoe lace and going back and forth.
The lead away cloth does a great job of removing the lead and powder build up at the end of the cylinder. I also use an ink (typewriter) eraser (I know, I am dating myself here) and rub out the "racoon eyes" on the cylinder face.
I was told back when I was a kid (60's) that you should clean your firearm right after you shoot it and then again a few days later. Might seem like overkill, but when your life depends on it, take it seriously.