The cap can be tested with your meter on the ohms range (red to plus side), or capacitance range, or by applying a voltage to it, in series with a resistor. If it is leaking (or shorted) the current flowing will create a voltage drop across the resistor.
I have a circuit I suggest people build to test zeners and STV diodes. I can be used to test low voltage cap leakage as well:
Use three 9v batteries, and you will get about 28vdc across the output. Connect the cap in place of the zener, with the plus side of the cap to the resistor. A 1kΩ resistor will charge up fast, and show a voltage drop across the resistor it the cap is leaking. A higher resistance will charge slower, but be more sensitive to the leakage current. A good cap will charge to the battery voltage (eventually) with no voltage drop across the resistor, if there is no leakage.
You will have to have the cap
out of the circuit to test it with this jig. It can be used to test in-circuit on zeners and STV diodes (with unit power off).
This eliminates the need for a dc bench supply, and you can stack as many 9v batteries as you need to get enough voltage to test caps, as long as you do not exceed the rated voltage of the cap.
For testing higher voltage zener diodes you need to have a voltage higher than the zener voltage.