Star pieces are found when stars fall from the sky. When a star falls, it makes a very loud "falling" sound, and a crash when it lands; they will then be apparent from a distance by bright rays of light. Walking over the fallen star soon after it lands will give you a star piece. 9 star pieces can be crafted into a Starstone and some experience.
If the star piece is left out too long, the star will become Star dust instead.
-9 Star pieces in a crafting bench with give you a Star stone
-1 Star piece in the crafting bench will give you 3 Star dust