You can break down a card into work by adding tasklists and tasks to it. You can add as many tasklists and task as you want and they will show up at your card as shown below. By pressing the tasklist button in the card-menu a tasklist will appear with one task already added.
You can click the empty square on any to task to mark it as done.
You can also click the name of any task to rename or delete the task.
Please note that during the time of writing, tasks don't aggregate towards any kind of completion status as a card's status is mainly determined by its location, be it in a backlog or board.