Here's one of many that will appear.
Black powder like Pyrodex breaks down in water, so the cheapest solvent is water mixed with a squirt of Dove dishwashing liquid.
If you are using a commercial solvent, make sure its designed for black powder.
For example, Hoppes #9 is for smokeless cartridge residue, and Hoppes #9-Plus is designed for black powder residue.
To start, take your solvent and wet a stack of patches. The patches should be moist to feeling-wet, but not dripping wet. Very wet patches can push solvent up into the breech passageway and possibly create misfires.
Set one on the muzzle and push it down with your range rod or cleaning rod. After going back in forth in sections of the barrel, flip the patch over and do the same thing.
Then, take a dry patch and do the same procedure using both sides to clean.
Clean at the same interval; after every shot, every other shot, etc.
Most serious target shooters agree that you should clean after each shot.
The cleaner the bore, the more accurate the shot will be.
Hope this helps.