There are many effects in Magic that cause multiple players to perform actions at the same time. Liliana of the Veil‘s first planeswalker ability is an example of this. When this ability resolves, each player in the game will discard a card.

At first glance it seems simple, but many players are confused on the order that the decisions are made and when actions are taken. When two or more players need to make a decision at one time, the active player makes his decision first, followed by each other player according to turn order. Then once these decisions have been made, the actions associated with these decisions are carried out.

What this means is that the active player (player that controls Liliana) will choose a card in his hand to discard first. He does NOT reveal it or give any information about this card to any other players. It is an acceptable and common practice to separate this card from the others in your hand by either holding it up or placing it face down on the table. Then the non-active player will do the same thing. Then both of these cards are discarded. It is only at this point when these cards are put into a graveyard that players will be aware of what other players have discarded. Let me reiterate, the non-active player will not be able to see what was discarded by the active player before he chooses what to discard.