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At the beginning of each player's upkeep, that player chooses target player who controls more lands than they do and is their opponent. The first player may search their library for a basic land card, put that card onto the battlefield, then shuffle.
The ability can only target an opponent of the current player.
The targeted player controlling more lands than the current player is a part of the targeting requirement. A player can’t be targeted by this ability unless it’s true, and the ability doesn’t resolve if it’s no longer true at that time.
Shuffling the library is part of the optional effect. The player only shuffles if they chose to search.
Because the “search” requires you to find a card with certain characteristics, you don’t have to find the card if you don’t want to.
The land card enters the battlefield under the current player’s control.
