Blackhorn 209: Do not use regular blackpowder substitute cleaners. Two good ones are Hoppes #9 or Montana Extreme cowboy blend cleaner. Don't use water or any water based cleaners. If you plan on shooting fairly soon, that is all you have to do. If you are not going to shoot for awhile, use a bore oil.
777: Water is really all you need, but you can use a lot of different cleaners. Regular windex or 50% alchol and 50% windex works well. I generally use a gun oil swabbing after cleaning, esp if I am using a water based cleaner.
With either cleaner, I soak a patch with cleaner and swab the bore, then I put a bore brush on and run that through the bore about 20 strokes. Then another soaked patch/dry patch/soaked/dry until they come out clean.
Next shooting session, you have to clean out the oil before you shoot or it will affect the flight of the bullet. To do that, I pop off 2 to 3 caps, then swab the bore with a dry patch and load. Still many times the first shot (in my experience) goes slightly different, so I do a "fouling shot" then load for target or hunting.
With BH 209, I have shot as many as 30 shots without swabbing once. With 777, I swab between each shot: one spit patch (yes, I actually lick the patch) and then a dry patch, then reload.
txhunter58
venor, ergo sum (I hunt, therefore I am)