Basically... all you do with those things is make sure that all of the connections are clean on the solenoid and the starter motor and make sure you have known good cables.
What I often do is drop the starter on the ground and hook it to a set of booster cables... then jump across the terminals while you hold the starter down with your foot. See if it works. If it doesn't work try hooking the pos cable directly to the starter motor terminal and see if the starter spins up. If it does... you've likely got a bad solenoid. More like bad internal contacts in it.
If you're real adventerous you can melt the solder off the terminals on the cap and take the switch apart, clean the terminals and put it back together. Otherwise you buy a new switch.