Check what the chip is on the bottom left of the driver board for the screen. That looks like one I have that runs on 12v, but you could probably get away with running it on a lower voltage. Best way to tell is to look at the listing that you got it from, they usually tell you what voltage they run at
As for hooking it up, if you want to stick with composite video, just connect a wire from the composite output of the wii to the input on the screen's driver board (check continuity with the outside metal on the connector to the two wires going into the board for one of the composite inputs, the one that isn't connected to the outer metal is the one for video signal in). If you want to use something else, that board looks like it can only take composite or VGA, so you'll have to get something like GC Video for Wii, or use some kind of component to VGA converter.