There are many ways to detect capacitors. Here are some common detection methods:

1. Use a multimeter to detect
Resistance mode detection:
In resistance "Ω" or ohm mode, connect the multimeter probes to the capacitor terminals (negative to negative and positive to positive).
The digital multimeter will display the value and then immediately return to OL (open line) or infinity "∞". If the same result is displayed for each attempt, it means that the capacitor is good.
For analog multimeters, short-circuited capacitors will show very low resistance, open-circuited capacitors will not show any movement (deflection) on the ohmmeter scale, and good capacitors will initially show low resistance and then gradually increase to infinity.
Capacitance mode detection:
When the multimeter has a Farad "Farad" for the capacitance "C" function, the capacitor can be tested in capacitance mode.
Turn the multimeter's knob to capacitance mode and connect the capacitor terminals to the multimeter leads (red to positive and black to negative).
If the reading is close to the actual value of the capacitor (i.e. the printed value on the capacitor container box), the capacitor is in good condition. If a significantly lower capacitance value or none is read, the capacitor is dead.
Continuity test mode:
In DMM (digital multimeter) and AVO (ampere, volt, ohm) meters, a continuity test mode is available.
Turn the knob and set the multimeter to continuity test mode, connect the positive (RED) probe of the multimeter to the anode (+), and the common (black) probe to the cathode (-) terminal of the capacitor.
If the multimeter shows signs of normal continuity (beep or LED light) and suddenly stops and displays OL (open circuit), the capacitor may be open circuit. If the multimeter LED light is on and a continuous beeping sound is emitted, it indicates that the capacitor is short-circuited.
Second, test with a voltmeter.
This method is applicable to polar and non-polar capacitors, and the nominal voltage value of the capacitor must be known. The voltage level is printed on the nameplate of the electrolytic capacitor, while the ceramic and SMD capacitors have specific codes printed on them. The test steps are as follows:
Make sure that a single lead (positive or negative) of the capacitor is disconnected from the circuit, or completely disconnected.
Check the rated voltage of the capacitor.
Charge this capacitor for a few seconds to the rated voltage (not the exact value but less than that). Make sure to connect the positive (red) lead of the voltage source to the positive lead of the capacitor and the negative to the negative.
Set the value of the voltmeter to DC voltage and connect the capacitor to the voltmeter.
Note the initial voltage reading on the voltmeter. If it is close to the supply voltage supplied to the capacitor, the capacitor is in good condition. If the reading is much less, the capacitor may be dead.
3. Measuring the time constant
If the capacitance value of the capacitor is known in microfarads (symbol µF) printed on it, and the capacitor is not fused and burned, the capacitor can be tested by measuring the time constant (TC or τ=Tau). The test steps are as follows:

When a capacitor is charged through a resistor of a known value, the time it takes for the capacitor to charge to about 63.2% of the applied voltage is called the capacitance time constant (τ=Tau, also known as the RC time constant). The calculation formula is: τ=R×C, where R is the known resistance value in ohms and C is the capacitance value.
Apply a known power supply voltage value and measure the time required for the capacitor to charge to approximately 63.2% of the applied voltage.
Calculate the capacitance value using the time constant formula based on the value of the given resistor and the measured time.
Compare the calculated capacitance value with the printed value. If the measured value is the same or almost the same as the printed value, the capacitor is in good condition. If there is a significant difference between the two values, the capacitor needs to be replaced.
4. Other detection methods
DC resistance test: Connect a resistor between the negative and positive terminals of the capacitor. When the capacitor meets certain capacitance conditions, measure the current at both ends to obtain a certain DC reference value, which is then compared with the nominal value. If it exceeds a certain range, it means that the capacitor is damaged.
Reliability test: Connect a fixed phase voltage to the positive pole of the capacitor and a negative phase voltage to the negative pole of the capacitor, and then measure the voltage change of the capacitor after a certain holding time. The quality of the capacitor can be judged by the change in the capacitance of the capacitor.
Waveform test: By connecting a continuous waveform to the positive and negative terminals of the capacitor and then measuring the voltage at the positive and negative terminals of the capacitor, it is possible to detect whether the capacitor has leakage or abnormal electrical parameters, thereby judging the quality of the capacitor.
Thermal aging test: By placing the capacitor in a high temperature environment and then comparing the capacitance parameters of the capacitor before and after high temperature, the quality of the capacitor can be judged.
Appearance inspection: Quality inspectors can perform an appearance inspection on the capacitor to determine whether the capacitor has obvious damage, such as cracks in the shell, burnout of the inductor chip, etc.
V. Precautions
Before testing the capacitor, be sure to ensure that the capacitor is fully discharged to avoid electric shock or damage to the multimeter.
When using a multimeter for testing, the appropriate range and mode should be selected according to the type of capacitor and test requirements.
During the test, pay attention to the readings of the multimeter or voltmeter, and judge the state of the capacitor based on the readings.
For high-voltage capacitors or large-capacity capacitors, additional safety measures should be taken during testing to ensure the safety of the tester.
In summary, there are many methods for capacitor detection, and the appropriate method can be selected for testing according to the actual situation. During the test, pay attention to safety and follow relevant operating procedures.