You can do a basic rail test pretty easy. The PSU needs to be loaded in order to test it meaning, you need to plug the ATX main harness to the motherboard as if you were running your PC normally. Set your volt meter to DC Voltage if it isnt an auto detect. The meter will say DCV usually or give the universal DC symbol of a flat line over a dotted line.
--Your Black lead should make contact with a PSU screw if your PSU is not mounted in the PC chassis. If it is mounted in your case already, any case screw that isn't painted should do.
--Your Red lead can be inserted into any molex connector/plug.
https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcQKc6qsCJIrxwn8CZNiDnq20PF-arhvQBrKtc36h37O3sFE5kPRdQ
Red = +5VDC
Yellow = +12VDC
These usually have a tolerance of +/- 10%
It is a bit more difficult to get other voltages because you need to tap into the main harness, while it is plugged into the mainboard. It is common safety practice to make live voltage tests using only one hand and remove all jewelry. You may need to use two hands if your ground lead/probe doesn't have an alligator clip. You can count the pins on your main motherboard harness and figure out which ATX plug it is. Then google it and you can find a pin-out for the wires. Sometimes the colors of the wires don't match the picture but the position on the plug should match the google picture assuming you have looked up the correct plug.