To participate in an Event Room click on the carasoul in the Main Lobby.  There are usually 2-3 Event Rooms running at the same time.

Playing in an Event Room is just like playing a normal bingo round, but you collect items that you can turn in for rewards.  

Once the game is over and you've collected your items, click on the "Prizes" tab to exchange your items for rewards.

Please note; all claimable items must be claimed before the event expires.  There is no feature or way to get back into an expired event and claim old rewards.