There are so many methods of cleaning and just as many as to when to clean. My carry or home defense guns get cleaned every time they are used, period. Others are not used as often so they get cleaned when I get to them but I don't let any of them sit without being cleaned for long periods of time.
As to cleaning methods, first off you don't want any kind of rod touching the interior of your barrel! Ever. That is what will wear the barrel out and older, improperly cleaned guns will show this wear. Most especially you don't want any part of the rod to contact the muzzle as this will destroy accuracy faster than anything else. Of course, if have an old, beat up shooter, it probably won't make any difference but you should still get in the habit!
Contrary to popular belief, if you have a match or hand lapped barrel, a bronze brush will leave tiny scratches in the barrel that are visible with a bore scope. Not something you could ever notice on a lumpy, chatter marked factory barrel and something that would literally take years to affect your accuracy but off hand, I would say that most benchresters only use nylon brushes and chemicals to clean their barrels and leave the bronze brushes to the pistol barrels. Especially if you shoot bare lead bullets, a bronze brush is a virtual necessity as there are no chemicals that will remove lead (ok, the electro-reverse plating will but it is not just chemicals!). Copper and carbon deposits can be removed from a barrel these days with just chemical action with no scrubbing necessary! How you apply them and how long you let them sit in the barrel is usually dictated by the rifle. I have a couple of rifles that like to be down to bare metal and some that like anywhere from 5 or more fouling shots before they settle in and shoot their best. Some will shoot a bunch of rounds before accuracy deteriorates and some will only shoot 20 before things get funky. You rifle will tell you what it likes if you listen well... and know what to listen for. Accurate rimfire guns are in a whole different category and often require the owner to jump thru all kinds of hoops to remain accurate. I'm talking really accurate, not your average 10/22 or Marlin factory rifle. But even those will often like a particular brand of ammo they will shoot especially well, if you're willing to go thru the process and look! If you are just plinking, any ammo will do! If you want minute of squirrel eyeball at 50 yards, it may take some work. And money! But that's a whole 'nuther ball game!
Keeping your guns clean and well maintained should be something every marksman wants. Those who never clean or just clean when the guns malfunction are just lazy, although that's actually ok these days as the quality of most modern firearms and ammunition allow that to be a thing. Whatever lights your candle or floats your boat. The only exception, in my opinion, is home defense or carry guns, which should always be cleaned and maintained after each use. After all, your life may depend on it!
Cheers,
crkckr