1. You can pick Shark, Yuma or Kaito/Kite as the character whose storyline you wish to follow.
2. Duel to collect Heart Pieces to complete the Heart.

3. The more Heart Pieces you have, the more events you can unlock, such as Yuma vs Tetsuo/Bronk, Shark vs Tetsuo/Bronk, and Kaito vs Yamikawa/Kaze.
4. When you collect 3 Heart Pieces to form a perfect heart, you advance to the Duel Carnival Finals.

Source: http://blog.livedoor.jp/maxut/archives/34127083.html