Usually, in MTG, when you play a card that requires multiple players to do something, like "Each player sacrifices a creature", players make choices in "APNAP" (active player / non-active player) order (going around the table in normal turn order if it's multiplayer), and then the effect itself happens simultaneously.
How does this work with hidden information? You'd still choose first, but when do you reveal the hidden information? Take, for instance, an "Everybody discard" effect (e.g. Liliana of the Veil): if I activate the ability, I'm supposed to choose a card first -- do I immediately show my card to the other players, or do I set it aside face-down until everyone has made a pick?