When Blightning resolves the targeted player will receive three points of damage and discard two card. The cards are discarded by the targeted player even if the damage is prevented or redirected to another player, creature or planeswawlker

If the targeted player does not have at least two cards in hand, they will do as much as possible and discard what they have. Similar to the what was mentioned in the above paragraph, if the targeted player does not have any cards in hand and does not actually discard, Blightning will still deal three points of damage.