breadboard - Getting 12V wall wart to power 12v solenoid driven by Arduino

Scenario: Power a solenoid by soldering on the gnd and pwr cables of a 12v wall wart.

I found this wall wart in my house that I think will work. From what it says I assume it can transform 120v to either 5v or 12v through the "tiny pins" that plugged into whatever device it plugged into.

I'm thinking the steps to use this wall wart on a breadboard to power both the solenoid and Arduino would be something like (with some unknowns?) [This is where I need help - verification and additional info on the steps to take]:

1. 
   

   Remove the "cruft" around the little pins so they are free (is there a recommended way of doing this?)

   
   


2. 
   

   Here is what I don't understand: take 1 of the 12 v little pins and solder a cable that will go from the wall wart to the breadboard's + row (or twist the 12V cables together then solder or crimp to cable) do the same with the GND.