I have modified the way I clean guns all these years. There is no proper way per se. We like what we like.
1. I only use nylon brushes made by hoppes. In fact I use them more as solvent spreader. I leave the solvent in the bore for at least 15 min before I patch. Give the chemicals a chance to do what they can do.
2. I used to push brush from the breech only. I stopped doing that real fast. All that unscrewing is pretty silly and tiring. In fact I only brush sparingly. Most of the time I just use soaked patch as spreader.
3. Tight patch pushed by a jag is not working well. If you want the patch to soak up fluid, it should be relaxed, not compressed. I like Otis pull through cables for that.
4. I don't clean guns after each use, not any more. Only do it when they are back to the safe for long period of time.
5. Stopped using bore guide. It helps somehow, but the hassle putting it on and storing it, I can do without.
6. Always wear gloves when cleaning guns. I am not as tough as other men, and I will be harmed by the chemicals and lead. Actually I put a plastic bag over the muzzle when I brush. It catches the fine mist when the brush exits.
7. Don't use hoppes #9 any more. That thing sucks.
That's just what I do. It may not be proper to you, but to me it is.
-TL