OK, let's break this down into a simple circuit. The battery voltage goes from the + post, though the starter fuse, though the big cable to the solenoid. The solenoid will act as a switch. From the solenoid, it goes though a "strap" to the starter motor. After going though the starter motor, it goes though ground, to the engine, though some kind of engine ground strap, back to the negative side of the battery. (You might want to check the ground path - make sure the starter has a good connection to the engine and the engine has a good connection back to the battery.)
When that small wire that's connected to the solenoid gets connected to battery voltage, the solenoid will pull in and turn on the starter motor. That wire in turn is driven by a relay in the underhood fuse box. An old mechanic test is to take a screwdriver and short the small wire to the big wire on the back of the solenoid. Things will get a little exciting as there will be a nice spark and the engine (should) start cranking. That's also the way I'd test it on a bench. Connect the battery to the big terminal and the ground, then short the small terminal to the big one.