Prizes for completed Challenges are sent via in-game message after those Challenges have gone through the voting process.

Tap the Person/fFce icon in the bottom right corner then tap on the Inbox tab to view your message. Scroll down and look out for your Challenge Results message and tap on it to open the message to retrieve the prize and automatically be added to your inventory.

You can find your prizes in your inventory by tapping on the Shopping Cart icon.