First of all, I'm not sure that this is an appropriate topic for the highly technical forum, as it seems more suited for the technical support forum.
But anyways, here goes:
The power switch on the back of an ATX power supply only turns on or off the 120-240VAC line voltage to the power supply. It's main function is to completely cut off AC power to the power supply, such as when you are working on your computer and you don't want the power supply to accidentally turn on if you touch the wrong things. When you turn on the AC power switch on the back of your power supply, the power supply then generates a +5V standby voltage. When switched by your motherboard (you press the power button on your computer), this +5V is used as a signal to tell the power supply to activate.
As such, you can see that you cannot ordinarily turn on your power supply just by using the switch on the back of the unit, as the power supply also needs the signal from the motherboard to tell it to turn on.
There ARE ways that you can hotwire the conductors on the ATX connector so that the power supply does receive the signal to turn on whenever there is AC power. It's very easy to do, and if you look around on the net you will find instructions quickly enough. However, there will be no load on the power supply...and it will be difficult to tell whether your power supply can operate properly when under load. There are many ATX power supply testers on the market that both make the power supply turn on and also provide an acceptable load (through the use of resistors to simulate the power consumption of a computer). These testers also measure the output voltages of the power supply and tell you whether the power supply is good. PC power and cooling and many others sell these devices. Of course, an oscilloscope would be the very best device for testing, as you could see the waveforms themselves....but I'll leave this out of the picture since it is beyond the affordability and range of most of us.
I still am not clear on what you mean by testing purposes. Testing of the ATX power supply itself to see whether it is good? If so, you are better off using one of the power supply testers above. If you mean for testing motherboards and/or computer systems.....as long as you knew the power supply was good, you would not need to do anything other than hook up the power supply to the motherboard and all other components like you would do normally.
Hope this helps, and good luck!