616.1e Once the chosen effect has been applied, this process is repeated (taking into account only replacement or prevention effects that would now be applicable) until there are no more left to apply.
Example: Two permanents are on the battlefield. One is an enchantment that reads "If a card would be put into a graveyard from anywhere, instead exile it," and the other is a creature that reads "If [this creature] would die, instead shuffle it into its owner's library." If the creature is destroyed, its controller decides which replacement to apply first; the other does nothing.
Example: Essence of the Wild reads "Creatures you control enter the battlefield as a copy of Essence of the Wild." A player who controls Essence of the Wild casts Rusted Sentinel, which normally enters the battlefield tapped. As it enters the battlefield, the copy effect from Essence of the Wild is applied first. As a result, it no longer has the ability that causes it to enter the battlefield tapped. Rusted Sentinel will enter the battlefield as an untapped copy of Essence of the Wild.