This is the way a starter works:
Turning ignition key applies voltage to the starter solenoid - usually inside the bump on the starter. The starter solenoid then activates. That is the click that you hear. The solenoid wire is relatively small compared to the starter wire. The starter wire is the very heavy wire coming straight from the battery. That wire usually has a high current fuse in it.
The solenoid will activate with a bad battery, but the starter won't turn as it takes too much current. If you turn your headlights on and they dim to nothing when you hit the key, it is a battery problem. If they do not dim, it is a starter problem.
Continuing.....The solenoid has 2 windings, both activate initially, then one drops out to hold the solenoid in. If one of the windings is open, the solenoid won't pull in all the way and the starter won't run. You will get a weak click sound. It may occasionally pull in and run the starter. I had this problem once.
When the starter pulls in all the way, it shorts two high current contacts and applies the battery voltage to the starter. The starter then turns. Those contacts could be bad/corroded.
The high current fuse could be blown. You can test this, if you can find it.
You could have a problem with the starter cable, or corroded battery contacts.
The starter winding could be open. You can't get to this point to test unless you disassemble the starter.
SO, do the headlight test first. If very dim, check for corrosion on the battery terminals.
If they don't dim excessively, then it is likely the solenoid, but check the high current line to the starter b4 you pull the starter.