How do general aviation airports inspect their runways?
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.