There are free gems hidden on each screen of Duel World. By tapping on certain background items, a little animation will play. If a special animation plays, between 1 and 5 gems will be awarded. This is random but each spot may work more than once a day.

To see the animations, tap on:
The fountain next to the Gate.
The lights leading to the PvP Arena.
The dome above the card Shop.
The trash can in front of the Card Studio.