Duels are initiated by visiting those marked arenas and before a duel, you are to choose your "Zoid", a pilot, and a special attack of sorts (I don't really know actually, since it's in Japanese). Duels, although presented in 3D (and are quite pretty) are fought over rock-paper-scissors style.
Winning duel will award you with more Zoids and more special attacks. It's a pretty simple premise for a pretty game. Even if it's not too much trouble for you to get around the game with some trial and error, it's not really worth buying the game at its full import price. Unless of course, there's a discount, but only hardcore Zoids fans..or Japan-o-philes need apply.
Zoids Battle Colosseum is available at Play-Asia for USD 14.90 with free international shipping to some countries. Click here for purchase details.