My 89 Sidekick has a clicky starter problem.   Will the sammy wire kit fix this or do I need a new starter?   Thank You,  

The first thing you need to determine is WHY is YOUR starter clicking - the Samurai clicky starter fix addresses only one out of a possible six problem areas, and one which is not normally a problem on a Sidekick (ever heard of the Sidekick clicky starter fix?  No?  Because no one makes it)

Possible problem areas are - weak or flat battery, loose or corroded battery connections, defective starter solenoid, defective starter motor, loose ground connection, and - this is the one the Samurai kit fixes - defective ignition switch or wiring.

i don't get that clicky starter fix stuff. how can that work?
your starter is probably pretty old.
brushes, bushings, solenoids, etc. don't last forever and will need servicing.
sometimes replacement is easier.

i don't get that clicky starter fix stuff. how can that work?

On the Samurai, the circuit that provides signal power to the starter solenoid is under-engineered.  As it ages, it is less capable of delivering sufficient current to move the solenoid with enough force to engage the electrical contacts.  The clicky starter fix is just a relay that is controlled by the starter circuit, and provides power to the solenoid directly from the battery.  It actually works pretty well...

It is a pretty common problem in a Samurai.  Not so much in the sidekick.