How do I clean my air gun?

When you get a new air gun you should carefully deep clean the barrel because most manufacturers put grease or preservative in the barrel so it does not rust in shipment. After that you should only clean the barrel when there is a problem with accuracy - not after every firing.

Pure silicone oil is very good for cleaning your air gun barrel, do not use cleaning fluids meant for regular firearms, they will ruin the seals in your air gun.

One of the most important things about cleaning an airgun barrel -- you rarely need to clean it. In field target shooting where many people shoot 10,000 or more pellets per year, the general consensus seems to be to clean only when accuracy seems to have degraded.

Most Airgun barrels are made from soft steel or brass!
Soft steel abrades very fast, and brass abrades even faster.
IZH Baikal air guns have much better hammer forged barrels just like a conventional firearm.

When you clean the bore of a gun, the cleaning rod can rub against the bore at the point where it enters the barrel. It will wear the barrel if it does rub. That's why you are warned to clean a barrel from the breech, if possible, so you don't wear the rifling at the muzzle.

Use a brush that is softer than the barrel
I suspect that RWS warns against using brushes to clean their barrels because so many shooters are careless when they clean. If you do use a brush, use one made of a material that's softer than the barrel of your airgun. For steel barrels, a bronze brush is fine. For brass barrels, there are nylon brushes, though I feel you should stay out of a brass barrel altogether unless there is a real problem.

Felt cleaning pellets
Felt cleaning pellets should not be used in a spring-piston gun. They do not cushion the piston sufficiently, and it is akin to dry-firing. You can use them in just about every other powerplant. If you do use them in a spring-piston gun, pack in enough felt pellets to provide some resistance when the piston comes forward. For an air gun with 800 to 1000 FPS power, perhaps five felt cleaning pellets in a row might be enough to cushion the piston.