When the triggered ability resolves, first the next opponent in turn order (or, if it's an opponent's turn, the opponent whose turn it is) decides whether or not to search their library and puts the land cards onto the battlefield as instructed. Each opponent will know what players before them did when deciding what they are going to do. Then each player who searched their library shuffles it.

Each opponent who searches their library may find between zero and three basic land cards. If they find only one, they put it onto the battlefield tapped under your control.