A search for "cleaning" in the subject line finds a number of previous discussions, including: this one.
I clean fairly often, so there isn't build-up of anything that some folks seem to have with ill-maintained firearms. What I typically use includes:
- Hoppe's #9 for bad bores, if needed.
- Break Free CLP spray, for general removal of crud/grease.
- Brass brushes, nylon brushes, patches + jig ... to remove the fouling once broken down by the cleaners.
- A bore snake. I use one dry, for cleaning the bore; and one lightly lubed with oil, for final prep.
- A good oil, such as Militec-1, Remington Oil, Hoppes oil.
- A good gun cloth, to wipe down the outside surfaces, for removal of fingerprints.