To cloak a card, put it onto the battlefield face down. It becomes a 2/2 face-down creature card with ward {2} and no name, mana cost, or creature types. It's colorless and has a mana value of 0. Other effects that apply to the permanent can still grant it any characteristics it doesn't have or change the characteristics it does have.
Vannifar, Evolved Enigma
A permanent that turns face up or face down changes characteristics but is otherwise the same permanent. Spells and abilities that were targeting that permanent and Auras and Equipment that were attached to that permanent aren't affected unless the new characteristics of the object change the legality of those targets or attachments.
You must ensure that your face-down spells and permanents can be easily differentiated from each other. You're not allowed to mix up the cards that represent them on the battlefield to confuse other players. The order in which they entered the battlefield should remain clear, as well as what ability caused them to be face down. (This includes disguise, cloak, and in games involving older cards, morph and manifest, as well as a few other effects that turn cards face down.) Common methods for doing this include using markers or dice, or simply placing them in order on the battlefield.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Jack Hughes
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
