Disconnect the air compressor from power and short each side of the run capacitor to ground to discharge it before touching the terminals. Remove the wires from the terminals on one side of the capacitor.
Set your meter on ohms and touch one probe to each side of the capacitor while watching the dial of the meter. The meter should read some resistance and rapidly climb in ohms, then it should count down to infinity and read open circuit. If you reverse the meter leads, the meter should do the same thing again. What you are reading is the capacitor charging and discharging on the battery voltage of the meter.
Check from each side of the capacitor to ground and you should read an open circuit. Any resistance to ground indicates a defective capacitor.
If you read anything except what was described, the capacitor is bad