Worn key cylinder has been my most common reason for not starting, but you might check some easy stuff first.
WARNING....CAR MUST BE IN NEUTRAL OR PARK WITH THE EMERGENCY BRAKE ON.
Remove the solenoid wire from the starter and attach a jumper wire to the positive terminal of the battery. Just touch the wire to the terminal as it will quickly spin the starter...or not.
Rarely will this be a problem, but you will know if the solenoid and starter are the problem.
More rare is the safety switches. Clutch switch on standard cars and a neutral safety switch for automatics. Auto matics will start in park or neutral...have you tried that?
Most common, at least for me is a worn key cylinder that does not allow the key to turn the switch far enough to engage the start circuit.
With over 300,000 miles on a car that I deliver pizza in, I use the key switch about 50 times a day so mine wearing out is expected.
removing the plastic under the steering wheel you will see the switch on the left as a circular black box.
Removing this, you can twist the switch with a screwdriver and I bet it will activate the starter.
This is a clear worn cylinder clue.
A new key switch from Autozone or such may fix it, but I just gave up and installed a pushbutton switch.
Hope this helps!
Bruce