the bit that pokes out is where the power goes.
Best thing I can suggest to you is this....
Get yourself an old (or cheap) 12v socket extension, it should have a positive and negative lead (seperated) going from the 12v plug over to the socket.
Cut the socket extension off so your left with the 12v plug and the two wires. Stretch them out (and cut one about an inch shorter than the other (this will protect the fuses).
Plug the 12v plug into the socket, and then touch the two electrodes (you can see through the plastic in the top pic). If you get them the right way around it will light up the light.
Then using Lenny's info above and attach a positive and negative wire to the spade connectors (crimp it) then attach it to the positive pole, and the same with the negative pole.
Then you just need to tap into the positive and negative wires of the centre as Lenny did.
If you are not confident with splicing into wires, I highly recommend the "PosiTap" (go for the red ones). These are so simple to use, and they put a single pin prick hole into the wire and tap into it to get power. They are the best I have found yet for keeping your wire in good health and giving a secure connection (I wish I had found them sooner!). I now use them for all my mods where I need to tap into a wire!