Let's see ... I will give it a try.
Batteries:
Try a 2 AA battery holder from Radio Shack. The battery holder will have two prongs on one end. One positive and one negitive. Connect the controller board red wire to the positive prong and the contoller black wire to the negitive prong. Solder the wires to the prongs. These batteries will power BOTH the contoller board and the servo.
Servo:
Connect the servo red wire to the contoller board blue wire, and the servo black wire to the contoller board yellow wire. Don't worry about the servo blue wire right now. Do not cut it off, just let it hang loose,
Transmitter:
Use whatever type and number of batteries the zip-zap transmitter needs, to provide power to the transmitter board.
That should power and control your servo. Try the switches on your transmitter to see if they work the servo. You may have to switch the red/blue and black/yellow wires to red/yellow and black/blue, if the servo spins in the wrong direction.
Keep us posted. 
Gator