Capacitor testing

Test with multi-meter that it is not short circuited.

Test with capacitance meter that capacitance value is correct.

If this is an electrolytic capacitor I measure ESR.

With some electrolytics I charge them to nominal voltage with power supply and measure charging leakage current or the rate it self duscharges.

If it is a small mains voltage capacitor I might test that it can withstand the needed voltage rating with insulation resistance tester at 250, 500 or 1000 VDC test voltage.