well.... make sure mower is out of gear, and spark plug wire removed (safer than getting run over) and use something to bypass the starter solenoid(jumper cables work well), this will tell you if its the ignition switch/starter solenoid or the starter
you can then run voltage to the solenoid trigger (small wire if theres only 3, if 4 then small one that goes back to ignition switch) if that clicks and turns the motor over, then its probably the ignition switch (or a wiring issue of it)