Curt..Bet ya still confused...
See if I can make it easier.
On the back of your ignition switch you will find a number of wires..find the one that goes to the S (start) terminal on your starter solenoid. It will be a heavy (12Gauge maybe) wire.
This wire needs to be disconnected from the S (start) terminal on the solenoid and connected to the neutral switch on your Trans. From the other terminal of the neutral switch on the trans, connect a wire (same size as the before mentioned wire) and route this wire and connect to the same terminal ( the start (S) terminal) on the starter solenoid, from where you removed the original wire.
What happens is this: If you are in neutral, the switch on the trans allows power to be passed to the starter..thereby starting the engine. If you're in gear, it wont allow power thru, thereby preventing the engine from starting whilst in a gear and running over ya dog.
When the fellas talk about a relay or a solenoid...they are referring to an electrical switch which is activated by power (as opposed to a switch you manually turn on). Relays and solenoids are used to switch large current draw components(starters, horns, fans etc), which use a current which would fry a normal switch. There is of course a manual switch which activates the solenoid/relay (ignition for example) but only needs to conduct relatively low power to switch the solenoid/relay which in turn switches the heavy draw component.
Whew!.....hope that helped
Les