All riding lawn mowers run on the same type of 12-volt circuit that an automobile runs on, and some of the parts are nearly interchangeable, such as the solenoid and starter. So exactly like an automobile, when the solenoid wears out or goes bad, it will not send any power to the starter. A clue to a bad solenoid is a clicking noise coming from under the hood, but checking the voltage at the solenoid is a sure way to troubleshoot the problem.
Turn the dial on your voltmeter to read 12 volts.
Attach the negative probe leading off of your voltmeter to either the chassis, a negative ground wire or the negative post on your battery.
Locate the positive wire that connects the solenoid with the starter. It will be virtually the only wire that runs from the solenoid to the starter post. Attach the positive probe from your voltmeter onto the positive wire leading off of the solenoid.
Turn the key on the ignition as if you were starting the riding mower and read the voltmeter. If the solenoid is bad, the meter will read little or no voltage, and the solenoid needs to be replaced. If the solenoid is good, you will get a solid 12-volt-plus reading on the meter. If the starter is not turning over at this point, it needs replacement.