Once an Event with a Leaderboard starts you can join them by reaching the minimum amount of tokens necessary to join the leaderboard.

Each event has a unique way to get tokens, so pay attention to its tutorial once it starts or hold the click on the token icon inside the event screen to see a tooltip teaching you how to get them.

Once you hit the minimum amount of tokens you will automatically join a Leaderboard and compete against other players to see who can gather more tokens during the event and receive the best rewards. The higher you get placed the best the rewards will be.