The following steps are completely safe if the following steps are done exactly as shown.

Do not under any circumstances open the case on any PSU! The capacitors in it will hold enough current to kill or severely burn you for several days even after powered off and unplugged.Unplug the PSU until instructed to plug it in.

This is meant to determine if a suspect PSU is bad or not and not meant to be a definitive PSU test tutorial.

Method One

Step One
1. Switch off the PSU if it has a switch and unplug it from the wall power or UPS. This must be done because even with computer powered off, the PSU is still on and has voltage present in its connectors.
2. Open the computer and locate the large power connector. It is normally on the right side of the motherboard.
3. Locate the locking tab on the connector, press it in to release and wiggle the connector and pull it out of the socket.
This is what it looks like and will have 20 or 24 pins and may be a white color.

Step Two

1. Bend a paper clip as shown in the illustration below.
2. Insert one end in the connector hole with the green wire and the other end to any one with a black wire. We have jumpered the green and a black conductor now.
3. See illustration above to locate the proper connectors.

Do not jumper ANY conductors other than GREEN and BLACK.

4. After jumpering the green and black conductors as shown above, plug in and switch on (if previously switched off) the PSU.
5. Check the PSU fan, it should be running now, if so the PSU is working. The case fans may run at this time which is normal. They may not run too which is also normal.
5. At this point if the PSU fan runs but the PC still won’t power on or has other issues, continue to method two below.

Method Two

1. Unplug the PSU. This method will use a Volt/Ohm meter (VOM) if available, to check the voltage out put. Leave the jumper connected. See illustration below.
2. Adjust the VOM to so it will read at least 20VDC, volts DC, direct current. Put the black VOM lead on any black conductor and the red on another color.
Yellow = 12VDC (11.4 – 12.6)
Red = 5VDC (4.75 – 5.25)
Orange = 3.3VDC (3.135 – 3.465)
These color conductors will have the same voltage on any of the PSU connectors.
3. Plug in the PSU and switch it on. Readings should be ± 5% (in red above) of the nominal voltages. In this picture the VOM is reading a 12VDC lead and shows 11.77 which is within specs and ok. If outside if these ranges, the unit is bad.
4. If the volts are within range but there are still problems, go to method three below.

Method Four

1. A better way to test a PSU is with a dedicated PSU tester like below. It will put a load on the PSU and test volts under load. This shows this PSU faulty due to 0VDC on the 12V 2 connector.
2. A PSU tester will automatically let you know if voltages are where they should be. Many will have an LCD display turn red for a bad PSU and emit a loud series of beeps.

To show a summary of test steps and options of methodology.

Common PSU Connectors

SATA drive power for hard drives and CD/DVD/BluRay drives.

EPS 12V which is usually plugged in near the CPU socket for CPU power.

PCIe for graphics cards. These may be 2×6, 1×6 + 1×8 and other configurations.

Common peripheral, Molex, connector for fans, lights and other case accessories. Adapters are available to use this for SATA, PCIe, and other connectors as well.

Floppy power connector, it is still on many PSUs.
You are done! This should determine whether this PSU is good or bad.

Reference: Power supply unit (computer – Search results – Wikipedia, the free encyclopedia

Also posted at 2xg's blog site