How to Get Starter Pins I'm not sure if 'starter pin' is the correct terminology.  When you buy a new chain, that doesn't have a master link, you get a longer pin that allows you to put the chain together.  Then you simply take a pair of pliers and snap the extra piece of pin off.  Is there anyway to just buy the pins without buying a new chain?
Yes. Any local bike shop should have them in stock, and they should cost no more than 5 dollars. You need to know the brand and type of your chain. (i.e. Shimano 10 speed or Campag 11 speed) If you know the model (i.e. Ultegra or Dura Ace Shimano, that is a bonus.

By the way, Shimano refers to it only as a reinforced connecting pin, or replacement connecting pin.