I basically use a ball bearing cleaning rod with the vfg adapter and those little vfg felt wads with JB bore paste.
First remove breech oring and clean the barrel as best I can with a patchworm and ballistol.
Then the JB, using smooth strokes from the breech end, with more strokes applied at the breech than the crown. Obviously be very careful when the patches are coming out the crown end - I make sure they never make it out all the way, to prevent damaging. Occasionally I've found subtle rough patches, which I also focus on. You'll see variations in how many strokes people recommend, but it really depends on whether you're just trying to subtly improve a good barrel (few) or save/resurrect a bad or ruined one.
After that, clean really well with the patchworm again, assemble and re-lead.
I've never had JB make a barrel worse, only better in terms of accuracy, fouling or both. Some have been revelatory - in particular my red wolf barrel which started out very good, but is now magnificent
Good luck!
PS - I see Nervoustrig has given a link while I was scribbling my post - his explanation is really good and better written than mine! Follow that and you won't go wrong
