You don't have to do anything to gather card histories; it all happens automatically.
Card histories are stored in three structures: acts, actions, and changes.
When a web request is made that involves transforming card data, it involves exactly one act. With the act we store a timestamp, an IP address, and, for signed-in users, the card id of the user.
Sometimes a single act involves adding or updating many cards, as when submitting a form for a structured card. For each card affected, Decko records an action. An action is always associated to an act, a card, and an action_type (create, update, or delete).
Every action involves one or more changes. A change is connected to an action, a field (name, type, content, or trash), and a value for that field.
When you look at a card's history, you are looking at the history view of that card. Like any views, you can use "history" in nesting or via the RESTful Web API. But the most common way to navigate to histories is via "view > history" on a card menu.
On each history view you will see a list of acts on the card. These are acts that involve actions on the card itself on on cards included by the card. Within each act you will see a short summary of the changes involved in each action associated with that act. You can use the triangle on the right to expand the act and see a much more complete version of the changes.