When Rootweaver Druid enters the battlefield, each opponent may search their library for up to three basic land cards. They each put one of those cards onto the battlefield tapped under your control and the rest onto the battlefield tapped under their control. Then each player who searched their library this way shuffles.
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.
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.