I've been shooting guns of all types for 40 yrs. and some of that has been in competition. All of the above posts are good, there are many good methods for cleaning a gun barrel.
The main thing, imo, is to clean every time you shoot your gun and use a bore guide. Most all the solvents, etc; will do the job. You can use a rod or boresnake/patchworm, they all work.
