Turn the heat pump's circuit breaker off. The correct circuit breaker uses a "Heat Pump" or "Air Conditioner" label. The circuit breaker labeled "Furnace" or "Air Handler" will not turn the power to the heat pump off.
Open the lid covering the heat pump's electrical connection box with an appropriately sized tool, usually a 1/4-inch or 5/16-inch hex-head screwdriver. The wires from the circuit breaker enter the heat pump's electrical connection box below its lid.
Locate the heat pump's capacitor(s). A heat pump's capacitor looks like a metal cylinder with two or three wire terminals exiting its top. Capacitors either mount to the electrical box's back wall or slide into a hole in the electrical box's floor.
Inspect the capacitor's housing visually. If the capacitor has a swollen or bulging top, or an out-of-square bottom, replace the capacitor. A bulging or swollen capacitor housing indicates the capacitor's internal plates do not align properly and the capacitor has failed or will fail.
Touch the side of the capacitor's housing. If the capacitor feels sticky or oily, replace the capacitor. A sticky- or oily-feeling housing indicates a faulty capacitor. Do not touch the capacitor's wire terminals, even after disconnecting the heat pump's circuit breaker.
Short the capacitor's terminals with a screwdriver. Place the screwdriver across both terminals in a two terminal capacitor. Hold the screwdriver on the terminal with a "C" or "Com" label and touch the "Herm" terminal then the "Fan" terminals on a dual capacitor. Shorting the terminals discharges the capacitor and makes it safe to handle.
Wrap each wire that connects to the capacitor with masking tape and write the capacitor's terminal label on the tape with a pencil.
Pull each wire from the capacitor's wire terminals with needle-nose pliers. Grab the metal portion of the wire's connector and pull straight up. Never pull on the wire itself.
Turn a multimeter to its highest resistance setting. A multimeter measures resistance in ohms.
Touch the multimeter's leads to the capacitor's terminals. Read the multimeter. The multimeter's reading should approach zero shortly after you touch its leads to the terminals, then the meter should adjust its reading steadily toward infinity. Replace the capacitor if it fails the resistance test. Test dual capacitors between the "C" or "Com" and both of the remaining terminals. Often only one side of a dual capacitor fails.