Basics on cleaning? Depends on what I've been shootin. If smokeless, I just put 'em back in the safe. If BP, they get cleaned with water, brush, patches, and then lube.
When they come all the way down, the parts get covered with bore butter during reassembly. But I only break 'em down about every 10,000 rounds or so, or about once every other month, or right before a big shoot. Next time will be right before EOT.
If they get wet, they come all the way down to make sure they are well dried, then any rust is worked off gently with 000 steel wool and oil, then they are cleaned up and lubed.
If there's leading, I'll use a Lewis Lead remover and one of those lead away cloths. Those work pretty good. For lube I normally just use Ballistol and Bore Butter. Though I slather the hinge parts of my SxS with white lithium bicycle grease.
That help?
Doc