The trick is to get the bore coated with a solvent, give it about 5 - 10 minutes to do it's chemistry thing and then use a cleaning patch to push the loosened fouling out. Continue with the patches until you get a clean one (or reasonably so) and you're done. Choke tubes sometimes require special attention, i.e., removal and separate soaking and scrubbing. But I only do that occasionally. Usually the procedure I described above is sufficient.
right after I've shot the last event of the day, I shoot a shot of Outers or Browning oil down the barrell(s) and then fog some on the outside and put the gun(s) away in thier case....then the next time they're taken out of thier case they are thoroughly swabbed out with my long fuzzy bore brush...I'll try soaking them and see what comes out!!