Irish Rose,
The wiring set up you described is typical and common. Once you have the dead foot controller apart all you need to do is clip the wires close to the original connections and then attach them to the new screws on the replacement foot controller. I actually solder ring connections to the wires so I get a much cleaner and stronger connection.
Foot controllers can be had at many places on line as well as your local dealer.
I have over 20 machines to sew on. From ancient to almost modern. Each of them has their own personalities and quirks. So when switching from one to the other I usually sew a bit on some scrap to re-familiarize myself with the one I'm using.
Joe