There will be a clue telling you where to get it. The key is a drop only when carrying the clue scroll. It disappears when used to open the chest or drawer. Keys are non-tradeable objects, specific to the player who finds them. They are used on all levels of treasure trails.
It is possible to obtain more than one key using the drop trick. However, after taking a clue from the chest/drawer, the key won't open it again, and the player gets a message The chest <(or drawer)> is locked. Keys obtained this way from the same clue will still remain in the bank; however, keys obtained from different clues will not stack.