Yes, you need a multimeter, but no don't buy one. Get one free from Harbor Freight with coupon. If somewhere without one, use the dome lamp as a poorboy's voltmeter. That will tell if battery and its terminals are OK.
Otherwise, search the many, many posts about "no start" on FABO.
Could be the key switch or bulkhead connector isn't getting 12 V to the yellow wire on the starter relay. Could be the neutral safety switch isn't getting grounded (bad switch, auto tranny isn't in P or N, or manual tranny doesn't have clutch pedal in, or switch or linkage needs adjusting). You can ground the NSS terminal for testing, but don't stand in front of the car, and insure the E-brake is on. You can also apply 12 V to the starter relay stud yourself and see if the starter contactor "clunks". I use a Magnum "mini-starter" for new starters.
