Delver of Secrets has a single triggered ability that involves a few steps. When it resolves, the controller of the Delver will look at the top card of his or her library. Then that player may choose to reveal the card. If the player does and the card is an instant or sorcery, the Delver will transform. Once the ability starts to resolve, all of these step happen before the opponent gets a chance to respond; you can’t wait until you see the card before deciding whether to try to kill the Delver, for example.

Whether or not this card is revealed, it is still on top of that player’s library during this entire process. Assuming that no other spells or abilities are played, the card will end up being drawn by its owner during the draw step. However, this ability triggers and resolves in the upkeep step, and the game will not advance to the draw step until both players pass priority without doing anything while the stack is empty.

This means that spells or abilities can change what the drawn card will be. If the opponent of the Delver’s controller does not want the revealed card to be drawn, he or she could play something like Dream Twist after the Delver’s ability has resolved. This will cause the revealed card to go to its owner’s graveyard before the draw step.