The small stud receives 12V from the key switch. The one large stud is hooked to the battery. The other large stud goes to the starter. When 12V is applied to the small stud, a set of contacts pulls together by magnetism and battery voltage travels through the solenoid to the starter.

It's a typical relay. Low voltage, and thin wires activate a coil inside, which creates a magnetic field and pulls a larger heavy duty set of contacts together until you release the key and the magnetic field ends.

Put an ohms meter on both large studs, one lead on each stud. Your meter will show OL. When you apply 12V to the small terminal, you might hear the contactors pull in and you will have 0 ohms between the two large studs.

to add to baymee's help, some starter solenoids get the ground connection for the 12 volt coil by direct case contact thru it's mounting fasteners to the tractor's frame. Others have TWO small posts, one being the coil ground lead; the other for 12v +. Hook yours up appropriately when testing.

Hopefully the image below might help.
You really can't TOTALLY "bench test" a solenoid without actually connecting it to a good 12V power source (battery).
If "bench testing" without a 12V power source, you can only test the small post (control wire) to solenoid body (or to second small post if applicable) circuit using an Ohmmeter to tell if the pull in coil is either open......or shorted.
But even if a solenoid tests good in that respect, it will not prove that the solenoid will actually operate because the solenoid moveable parts inside it might be stuck physically and not close the circuit when it should.
The image below depicts the most commonly accepted way to evaluate the condition of a starter solenoid.
You must understand that a solenoid in this usage is just a very large electrical switch necessary to carry the enormous (relatively speaking) electrical load the starter uses to operate.
The small post on the solenoid operates the solenoid to complete the starter circuit so the starter can spin.

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