You can earn prizes in a number of different ways!
1 - Chapter rewards are given out for actively following the story along with the rest of Neopia during the three-week time period over which each chapter is released.
2 - Some prizes are earned by playing and advancing through specific minigames or Battledome challenges (or donating your time to the Neopian Hospital)
3 - Other rewards can be unlocked by participating in the ongoing community activity of collecting more void essence for Dr. Landelbrot to continue his research.
4 - Hidden trophies or fearless deeds that can be acquired through acts of valour going above and beyond that of ordinary Neopets.