How do general aviation airports inspect their runways for cracks, ruts, holes or anything that would impair their integrity? How often do airport operators conduct standard inspections of their runways as well as taxiways and ramp areas?
Runway inspection is usually performed visually. In this answer there is a list with several items which have to be checked in EGNX, but the frequency and exact list check items will be different at each airport. I'm not aware of any binding standard.
In every GA airport I know there is at least one daily inspection performed shortly after sunrise (or before the airport becomes active). This is especially important in grass airfields, where wild boars could have dug holes at night. If something happens during the day there is normally someone who sees it and can either inform the operator or fix it himself. Larger airports operating at night will probably inspect the runway more often.
This video will answer your question, a reporter join one of the 4 daily runway inspections at Zurich airport. Each GA airport has its own rules about these inspections as it is the responsibility of the airport to provide a safe place for aircraft to land.
The main threat is debris on the runway which can have disastrous consequences. https://en.wikipedia.org/wiki/Air_France_Flight_4590