First, everyone shuffles their stacks out of sight, so no one can tell who played which card.
Then, starting with the player to the dealer’s left, each player reveals their stack, suffering or benefitting from those cards’ effects.
Any decisions that must be made — like whether to pay for a Hit and who to use it on — are made by that stack’s owner before the next player’s cards are revealed or resolved. (To be clear, decisions are made by the player the card was played on, not necessarily by the player who played the card.)
It’s worth noting that it never matters what order a given stack’s cards are revealed or resolved in. They can always be resolved as a group. (Rare exception: If Crime and Hit appear to be in conflict, see “Hit Card Timing”.)
Revealed cards are discarded after being resolved, unless their effects say they are banked instead.