Step 1: A Trip to Your Toolbox
1) An old motherboard
2) A (preferably old) power supply
3) The rest of the parts to function with your motherboard
The tools you will need are basically these:
1) Wire cutter
2) (preferably) Soldering iron
4) Insulation tape or shrink tubing.
You might want a screwdriver in case you want to take out your power supply to easily work on it.
Once you have the above materials you can get started.
Step 2: Some Useful Knowledge
When you switch on the mains power to your computer (when you press the switch on your UPS, or insert the plug in a socket), the power supply gives a +5V supply to the motherboard for minimal functionalities, such as for the power button to work and for things such as Wake-on-Lan, etc. (you will also get the LED on), this power is sent over the purple cable. When the motherboard wants to switch on (for example if you press the power button) it grounds the PS_ON# cable of the power supply to the black cables, the PS_ON# cable is the green one. At this point the power supply switches on and supplies power to all the items in your computer, when the voltages are all stabilized, it sends the PWR_OK signal to the motherboard over the gray cable. When your computer shuts down and the OS sends the power off signal, the motherboard disconnect the PS_ON# cable from the ground and therefore your system will power off. So if you know your power supply works, but when you press the power button your computer doesn't start, you understand that it is you motherboard that is not giving the PS_ON# signal to your power supply. What I will demonstrate is practically how to manually send the PS_ON# signal to the power supply ourselves. If you want to know more about how power supplies work, you can see this two links which I found:
Step 3: Enough Talking, Let's Do It!
1) With the wire cutters, cut the GREEN cable coming from the power supply to the motherboard connector.
2) Cut one of the BLACK ground cables at the same height as you cut the green one.
3) If you are going to use the heat shrink tubing, insert it now on the end of the BLACK cable that goes to the motherboard.
4) Using the soldering iron, solder the two ends of the BLACK cable plus the end of the GREEN cable that goes to the POWER SUPPLY together.
5) If you were using heat shrink cover the joint and shrink the tube, or if you are using insulation tape, simply wrap the tape around the joint.
6) Cover the end of the GREEN cable that goes to the motherboard, we will leave that end disconnected.
7) Plug your power supply into the mains without connecting the motherboard and see if the fan starts to spin.
8) If the fan did spin, connect the PS back to the motherboard, make sure you have RAM, CPU, etc. in the motherboard, plug in the mains again and hope it will all work.
9) In case you don't have a UPS which you can switch off to cut the mains input, you can add a switch to the front of your computer to do so (see the next step).
Yeah, I know, the steps above sound a bit confusing, no? Then you can try following the pictures. If you still have trouble just leave a comment and I'll help you. :-)
Step 4: A Few Little Inconviniences
If you want to make the shutdown procedure more elegant, you can try disabling ACPI features in your OS or BIOS, in that case you will get a message saying "It is now safe to switch off your computer".
Wish you a good luck if you try this out!