How often should I clean an airgun barrel?

Less often than you would expect. Most airgun barrels run best with a thin film of lead deposited from previous shots, and many shooters never clean their barrels at all.

The right time to clean is when accuracy clearly degrades from its baseline, typically anywhere from 500 to several thousand shots depending on barrel, pellet, and velocity. Higher velocity (above 900 fps) and harder pellets (with antimony) lead more quickly. Use cleaning pellets, a pull-through with a patch, or a quality coated rod from the breech end.