All starters on riding lawnmowers get their electricity from the on-board battery. The circuit begins at the ignition key, and just like starting a car, once the key is turned, it completes the circuit through a solenoid -- which acts like an electrical connector -- and sends power to the starter, causing it to spin the flywheel, which starts the engine. To test a starter, all you need to do is bypass the ignition circuitry.
Lift up the bonnet of your riding lawnmower and locate both the battery and the starter.
Find the electrical posts where the wires are attached on both the battery and starter. The red wire is "hot" and the black wire is the "ground."
Brush off the posts with your stiff-bristled brush, removing all dirt and debris. This will assure a solid electrical connection.
Put on your rubber gloves. Attach one end of the black cable from your jumper to the black wire or negative post on the battery. Attach the other end to any metal part of the tractor.
Attach one end of the red cable to the red or positive post of the battery.
Touch the other end of the red jump lead to the positive-red side of the starter. If the starter is good, it will turn over. If the starter is bad, it will not turn over and must be replaced.
When jumping a starter like this and it engages, you will know instantly if it works, and you can remove the cables and troubleshoot the rest of the circuitry for any problems.
Although you are only dealing with a 12-volt system, always wear rubber gloves when testing a starter. Rubber is the best way to insulate skin from getting a nasty little shock and even though 12 volts won't do any real damage, getting shocked by a riding lawnmower battery isn't a pleasant experience.