Ok, attached is a picture of the starter relay for an automatic car (assumes your's is). It should be mounted on the firewall near the brake booster (or driver side of firewall). There will be two big cables going to the studs on the right side from the battery and starter. Using a screw driver or anything metal, bridge the two connections and the car should start. Caution, sparks will fly so be prepared, but the car should start. Hold the bridge on the relay until the car starts. It will turn over and over until enough gas is in there and it starts. If you have a remote starting trigger you can hook the alligator clips to these two studs and start the car with the trigger. If this works, you know the relay is good.
Next thing to do is hook up a long wire with alligator clips to the bottom tab on the left side (relay ground) and connect other clip to the negative side of battery. Then try starting the car. If it starts, then most likely the neutral safety switch is bad down at the tranny.
Now down to the transmission. On the driver side of the tranny, above the pan rail, perhaps in the middle of the tranny case will be the below. It will have a corresponding 3 wire connector on it. Pull the connector off and you will see the 3 pins. The middle pin is the ground. To test the ground, use your multimeter on the continuity function and touch one probe to the middle pin and the other probe to the tranny case. It should beep if its grounded properly. If not, there's the problem and time for a new neutral safety switch. (of course when jacking up the car to get to the neutral safety switch, please use safety common sense and jack stands.
Oh, and get a test light, its invaluable with these old cars!!
Oh, another thing. If the neutral safety switch is bad and you need a new one, BEFORE installing the new one, remember to drain the transmission fluid or you'll get a bath when you take out the safety switch (ask me how I know). Hopefully your tranny pan has a drain plug!