I'm not sure if you can fully test the capacitors (that is, ESR) with just a DC power supply...usually also need a signal generator for that (gets complicated), or else a dedicated tester (easy).
You can test the 'lytics capacitance if you have an assortment of resistors along with the power supply.
The time constant for charging a capacitor is its capacitance in farads, times the series resistance in ohms, that you are charging it through. That is, R x C. It takes 5 time constants to full charge a capacitor though a resistor.
The easiest format is to use a high impedance analog meter if you have one, but a DMM can do it. Discharge the capacitor fully, and connect the meter across the capacitor. The capacitor is then hooked to a DC supply through a high value resistor. (Mind polarity of the capacitor and the analog meter, and don't exceed the voltage ratings of either.)
You turn on the power count the seconds until the voltage stops rising across the capacitor indicating that the cap. is fully charged, and divide that by 5 times the ohms of the resistor. That is the capacitance in farads.
For testing leakage, you hook a 10M ohm DMM in series with the discharged capacitor and the power supply. Read the voltage and use ohm's law to determine the series resistance of the capacitor's dielectric. The power supply should be set to close the working voltage of the capacitor, but not more. (Mind polarity as always.)