Uncoil the wires from around the solenoid assemblies, and bring the unconnected ends together. You're going to want to twist these together, so that each twist has one wire from each solenoid (see second picture). If you're using speaker wire like I am, twist the two silver parts together, and twist the two copper parts together.
The next part will sound complicated, but it's very easy. Starting at the top of the picture and working counter-clockwise, we're going to:
- connect one set of the wires from the solenoid to the black wire of the AA battery pack
- connect the red wire of the AA battery pack to the black wire of the 9V battery pack
- connect the red wire of the 9V battery pack to one post of the foot switch
- connect the other solenoid wire to the other post of the foot switch
That's it! It doesn't matter which pair of solenoid wires you use, or which part of the foot switch you use. You can just twist the wires together and cover them with electrical tape, but your project will be much more durable if you solder and insulate these connections. If you're using the 12V adapter, use the black wire of it in the first connection, skip the second, and use the red wire for the third connection.