That LOOKS like quite a nice power supply, and would be very useful in some circumstances.
IF you were wanting to operate your PC from 12 Volts DC then this is a suitable supply for you.
But IF you want to operate it from AC mains you should sell / give this to somebody else and obtain a more normal power supply - because adding a mains to 12V conversion stage will introduce extra problems that you are unlikely to want to deal with.
You should be able to connect a 12V car battery or 12V DC adaptor of sufficient power output capability to operate it.
Red connects to +12 VDC.
Black connects to ground = -12VDC.
They say that it supplies up to 200 Watts of power.
To supply this much power you would need say 250 Watts input.
At 12 Volts that's about 20 Amps.
That is a large amount of current for typical 12V supplies.
A LARGE 12V truck battery charger may supply that.
Even at half power you would need about 10 amps - also more than most supplies are capable of.
Your motherboard needs to support the connector shown - they say it will work with any Pentium 4 motherboard but that it is specifically made for use wih mini-ITX motherboards
The power supply was apparently sourced from here.