I usually give things a wipe down with a soft cotton rag before putting them back in the cases at the range. Once home, I'll break things down, bore snake the barrels a few times and then use either Hoppes 9, Elite or S&W synthetic cleaner depending on the firearm on the carbon and in the barrels.

While it's soaking, I'll pop the primers, stroke the pockets and put the shells into a dry tumbler with some walnut.

Once I'm done with that I go back to the firearms and wipe off/swab the barrels of the cleaners. I'll repeat both if necessary till they wipe/swab clean.

For any hard to reach places, I use Q-tips, nylon tooth brushes and nylon dental picks.

Most times I'll blow things out with my air compressor then a wipe down before oiling and lubing and final wipe.

I have all rifle bore snakes as I can use them for both. I also have multiple one piece cleaning rods, bronze brushes and jags. On occasion (every few years) I'll go to town on my stainless cylinder faces with mothers billet polish and a cotton t-shirt, just because.