You can earn prizes by collecting points in the Altador Cup! The main way this can be done is through playing Altador Cup games (Yooyuball, Shootout Showdown, Make Some Noise, and Obstacle Course Caper), but you can also earn points through completing Achievements and answering Trivia questions during the Press Tour. Basically anything you do to earn points for your team will also earn you Prize Points and Challenge Track points! It's all connected.
Prizes must be claimed on the Challenge Track or Champion's Track. There's no time limit for claiming prizes, so you can collect them immediately, collect a few at a time, or wait to collect them all at once!