The first step is always clean the battery terminals - that means disconnect them and scrape them till shiney metal is showing. If the terminals are dirty, lights etc. can still work because they are low current devices, unlike the starter which takes a lot of amps to spin it.
If that doesn't correct it, you can troubleshoot the starter pretty easily. According to the shop manual, the starter solenoid is mounted on top of the voltage regulator. Make sure the car is in neutral and the brake set (or wheels blocked) then take a jumper cable, or thick jumper wire, and connect one side to the neg battery terminal (assuming the battery is connected positive ground as originally) and touch the other side to the small terminal on that solenoid. If the starter spins, then the problem is the starter button or wiring to it. If it does not spin, take a set of regular jumper cables and connect one side to the neg terminal on the battery and the other side to the large terminal which goes from the solenoid to the starter. The starter should spin. If it does, the problem is the solenoid or the wiring to it. If it doesn't, then it's the starter or a bad connection to it, or a bad ground. It takes a lot of amps to spin that starter and corrosion can cause problems. Give those things a try and let us know how it goes.