Thats great! Here is your homework;
First set the meter to volts DC. Attach or hold the black wire to the negative terminal of the battery. Hold the red terminal to the positive terminal of the battery . You should see that it reads 12 volts (or a little higher, normal is 11.5 to 13.5 volts DC)
Next take the black lead and hold it to the frame of the tractor. The frame is connected to the negative terminal and should give you the same reading as the battery test. You will notice that if you touch a painted surface you will not get a reading, but if you touch bare metal you will get the reading you are looking for. This is true for all the tests we are about to perform. All tested surfaced need to be clean of paint, rust, corrosion and dirt.
Now that you know how this works let's get to testing the system. The black lead will always go to a good clean ground in all these tests.
Test one - follow the positive battery cable to the starter solenoid (#43 it looks upside down in the picture) and test for voltage. You should have 12 volts
Test two - there is another large stud with a large wire on the solenoid, this goes to the starter. For this test you need a helper. With your helper sitting on the mower, clutch in and blades off have them hold the key in the start position and check for voltage at the starter side of the solenoid, you should have 12 volts
Depending on what you find we will continue from there. I am including a picture of a typical starter solenoid for you to aid in finding it easier.