How do I wire this power supply? It doesn't seem to have any connections and in my mind, it needs two for mains voltage, 2 for 12v out.
The photos show that this supply has had wires soldered for mains input and 12V out, but they have been cut off.
Consider if you really want to buy a product of unknown origin that has no instructions and may be cut off from another product, or would you rather want to buy a real product whose safety is guaranteed by a reputable manufacturer and it comes with instructions how to use it.
Oh and in general, you should ask the seller. This is not a support forum for random ebay products.
Edit: It seems the mains input connections on the bottom of the PCB may not be wires after all but metal springs. If so, it means that that PCB is supposed to be in a wall wart type of case where the mains inputs connect to the springs when the PCB is in place. So anyway using this outside of such a case requires manual work to hack reliable mains input to this device, and since any hacks involving mains can be dangerous and lethal, I suggest not to modify it due to safety and legal consequences (if it burns down a house or someone touches it).